# S. K. ChaubeyUniversity of Technology and Applied Sciences-Shinas Oman · Department of Information Technology (Section of Mathematics )

S. K. Chaubey

Doctor of Philosophy in Mathematics (Differential Geometry and its Applications)

## About

104

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747

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Citations since 2016

Introduction

Additional affiliations

January 2016 - November 2017

## Publications

Publications (104)

The goal of this paper is to investigate the existence of non-trivial solutions for Fischer–Marsden equation (FME) within the framework of (2n+1)-dimensional cosymplectic manifolds. It is shown that the existence of such a solution forces the metric to be a gradient η-Ricci soliton. We also explore the geometrical properties of gradient Ricci solit...

In this paper, we study the properties of -Kenmotsu manifolds if its metrics are -Ricci-Yamabe solitons. It is proven that an -Kenmotsu manifold endowed with a -Ricci-Yamabe soliton is -Einstein. The necessary conditions for an -Kenmotsu manifold, whose metric is a -Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an...

In the present paper, we characterize 3-dimensional Riemannian manifolds M3 admitting Ricci-Yamabe solitons (in short, RYS). It is proved that if an M3 endowed with a semi-symmetric metric ζ-connection admits a RYS, then the scalar curvature of M3 satisfies the Poisson equation
∆ r= 8 (2α− 3β− ϱ) β
, where α, β∈ R and β= 0. We also discuss the exis...

In this article, we derive Chen’s inequalities involving Chen’s δ
-invariant δM
, Riemannian invariant δ(m1,⋯,mk)
, Ricci curvature, Riemannian invariant Θk(2≤k≤m)
, the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the ob...

This research article attempts to explain the characteristics of
Riemannian submersions in terms of almost η-Ricci-Bourguignon soliton,
almost η-Ricci soliton, almost η-Einstein soliton, and almost η-Schouten
soliton with the potential vector field. Also, we discuss the various conditions for which the target manifold of Riemannian submersion is η-...

The focus of this paper is to characterize the Lorentzian manifolds equipped with a semi-symmetric non-metric ρ-connection [briefly, (𝑀,∇̃)]. The conditions for a Lorentzian manifold to be a generalized Robertson–Walker spacetime are established and vice versa. We prove that an n-dimensional compact (𝑀,∇̃) is geodesically complete. We also study th...

In the present paper we study the properties of α-cosymplectic
manifolds endowed with ∗-conformal η-Ricci solitons and gradient ∗-
conformal η-Ricci solitons.

We explore “the horizontal lift” of the structure J satisfying J 2 − α J − β I = 0 and establish that it as a kind of metallic structure. An analysis of Nijenhuis tensor of metallic structure J H is presented, and a new tensor field J ˜ of 1,1 -type is introduced and demonstrated to be metallic structure. Some results on the Nijenhuis tensor and th...

This research article attempts to investigates anti-invariant Lorentzian submersions and the Lagrangian Lorentzian submersions $(LLS)$ from Lorentzian concircular structure [in short, $(LCS)_{n}$] manifolds onto semi-Riemannian manifolds with relevant non-trivial examples. It is shown that the horizontal distributions of such submersions are not in...

We set the goal to study the properties of invariant submanifolds of the hyperbolic Sasakian manifolds. It is proven that a three-dimensional submanifold of a hyperbolic Sasakian manifold is totally geodesic if and only if it is invariant. Also, we discuss the properties of $\eta$-Ricci-Bourguignon solitons on invariant submanifolds of the hyperbol...

f(R,T)-gravity is a generalization of Einstein’s field equations (EFEs) and f(R)-gravity. In this research article, we demonstrate the virtues of the f(R,T)-gravity model with Einstein solitons (ES) and gradient Einstein solitons (GES). We acquire the equation of state of f(R,T)-gravity, provided the matter of f(R,T)-gravity is perfect fluid. In th...

In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector...

In this paper, we give a complete classification of Yamabe solitons and gradient Yamabe solitons on real hypersurfaces in the complex quadric Qm=SOm+2/SO2SOm. In the following, as an application, we show a complete classification of quasi-Yamabe and gradient quasi-Yamabe solitons on Hopf real hypersurfaces in the complex quadric Qm.

The aim of the present work is to study the properties of
three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a
Yamabe soliton. It is proved that every three-dimensional Lorentzian
para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian
para-Ke...

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold
equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown
that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized
quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential
vector field ζ...

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then t...

Purpose
The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type ( α , β ) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α -Sasakian manifold, Lorentzian β -Kenmotsu manifold and Lorentzia...

We establish the geometrical bearing on Legendrian submanifolds of Sasakian space forms in terms of r-almost Newton–Ricci solitons (r-anrs) with the potential function \(\psi : M^{n} \rightarrow \mathcal {R}\). Also, we discuss the Legendrian immersion of Ricci solitons and obtain conditions for L-minimal and totally geodesic under Newton transform...

The main goal of this manuscript is to study the properties of
3-dimensional hyperbolic Kenmotsu manifolds endowed with Yamabe and
gradient Yamabe metrics.

In this research paper, we develop the geometrical bearing on
Legendrian submanifolds of Sasakian space forms in terms of r-almost
Newton-Yamabe Soliton with the potential function ψ : Mn −→ R. Also,
we examine the certain conditions for L-minimal and totally geodesic
Legendrian submanifolds of Sasakian space form admitting the r-almost
Newton-Yama...

In this paper, we characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.

In this manuscript, we give the definition of Riemannian concircular structure manifolds. Some basic properties and integrability condition
of such manifolds are established. It is proved that a Riemannian concircular structure manifold is semisymmetric if and only if it is concircularly
flat. We also prove that the Riemannian metric of a semisymme...

We study the properties of Lorentzian para-Sasakian manifolds endowed with *-Ricci solitons and gradient *-Ricci solitons. Finally, the existence of *-Ricci soliton on a 4-dimensional Lorentzian para-Sasakian manifold is proved by constructing a non-trivial example.

Our aim is to characterize the Lorentzian manifolds endowed with a type of semi-symmetric non-metric connection. It is proven that a Lorentzian manifold with a type of semi-symmetric non-metric connection is a GRW space-time. To minimize the gap between the RW space-time and the GRW space-time, we establish a bridge between them. It is shown that a...

The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies $\mathfrak{L}^{*}_{g}(\lambda)=0$ on a $(2n+1)$-dimensional Kenmotsu manifold $M^{2n+1}$, then either $\xi \lambda=- \lambda$ or $M^{2n+1}$ is Einstein. If $n=1$, $M^3$ is locally isometric to the hyperbolic...

Purpose
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η -Ricci solitons and three-dimensional weakly symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional prop...

We characterize the three-dimensional Riemannian manifolds endowed with a semi-symmetric metric ρ-connection if its Riemannian metrics are Ricci and gradient Ricci solitons, respectively. It is proved that if a three-dimensional Riemannian manifold equipped with a semi-symmetric metric ρ-connection admits a Ricci soliton, then the manifold possesse...

This paper deals with the study of perfect fluid spacetimes. It is proven that a perfect fluid spacetime is Ricci recurrent if and only if the velocity vector field of perfect fluid spacetime is parallel and α = β. In addition, in a stiff matter perfect fluid Yang pure space with p + σ ≠ 0, the integral curves generated by the velocity vector field...

In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1; 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-sym...

The object of the present paper is to study some classes of N(k)-quasi Einstein manifolds. The existence of such manifolds are proved by giving non-trivial physical and geometrical examples. It is also proved that the characteristic vector field of the manifold is killing as well as parallel unit vector fields under certain curvaturerestrictions.

We set a type of semi-symmetric metric connection on the Lorentzian manifolds. It is proved that a Lorentzian manifold endowed with a semi-symmetric metric ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odd...

The objective of this study is to investigate η-Einstein solitons on (ε)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of η-Einstein solitons on φ-symmetric (ε)-Kenmotsu manifolds.

We set the goal to study the properties of perfect fluid spacetimes endowed with the gradient η-Ricci and gradient Einstein solitons.

The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account , a new generalized symmetric me...

We characterize the three-dimensional Riemannian manifolds equipped with a semi-symmetric metric-connection under the assumption that the Riemannian metric is a Yamabe soliton. It is shown that a three-dimensional Riemannian manifold endowed with a semi-symmetric-connection, whose metric is Yamabe soliton, is a manifold of constant sectional curvat...

The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.

We classify almost Yamabe and Yamabe solitons on Lorentzian
para (briefly, LP) Sasakian manifolds whose potential vector field is torse-forming, admitting a generalized symmetric metric connection of type
(α, β). Certain results of such solitons on CR-submanifolds of LP-Sasakian
manifolds with respect to a generalized symmetric metric connection ar...

We characterize almost co-Kähler manifolds with gradient Yamabe, gradient Einstein and quasi-Yamabe solitons. It is proved that if the metric of a [Formula: see text]-almost co-Kähler manifold [Formula: see text] is a gradient Yamabe soliton, then [Formula: see text] is either [Formula: see text]-almost co-Kähler or [Formula: see text]-almost co-Kä...

We introduce and study quasi hemi-slant submanifolds
of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant
submanifolds of cosymplectic...

Sasakian manifolds with respect to a non-symmetric non-metric connection are
studied. Some properties of the curvature, the conformal curvature, the conharmonic curvature of Sasakian manifolds admitting a non-symmetric non-metric connection are studied. Semisymmetric and Ricci semisymmetric Sasakian manifolds with respect to a non-symmetric non-met...

The object of the present paper is to study the properties of three-dimensional Lorentzian concircular structure ((LCS) 3-)manifolds admitting the almost conformal η-Ricci solitons and gradient shrinking η-Ricci solitons. It is proved that an (LCS) 3-manifold with either an almost conformal η-Ricci soliton or a gradient shrinking η-Ricci soliton is...

The aim of the present paper is to study the properties of locally and globally φ-concircularly symmetric Kenmotsu manifolds endowed with a semi-symmetric metric connection. First, we will prove that the locally φ-symmetric and the globally φ-concircularly symmetric Kenmotsu manifolds are equivalent. Next, we will study three dimensional locally φ-...

The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian
space-forms. We deduce some results related to the invariant and
anti-invariant slant submanifolds of the generalized Sasakian space-forms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical...

In paracontact geometry, we consider η-Ricci soliton on η-Einstein para-Kenmotsu manifolds (M, ϕ, g, ζ, λ, µ, a, b) and prove that on (M, ϕ, g, ζ, λ, µ, a, b), if ζ is a recurrent torse forming η-Ricci soliton then ζ is concurrent as well as Killing vector field. Further we prove that if the torse forming η-Ricci soliton on (M, ϕ, g, ζ, λ, µ, a, b)...

The object of present paper is to study some geometrical properties of quasi Einstein Hermitian manifolds (QEH)n, generalized quasi Einstein Hermitian manifolds G(QEH)n, and pseudo generalized quasi Einstein Hermitian manifolds P (GQEH)n.

The aim of the present paper is to study the properties of three-dimensional Lorentzian concircular structure manifolds ((LCS) 3-manifolds) endowed with almost η-conformal Ricci solitons. Also, we discuss the η-conformal gradient shrinking Ricci solitons on (LCS) 3-manifolds. Finally, the examples of almost η-conformal Ricci soliton on an (LCS) 3-m...

We set the goal to study the properties of LP-Sasakian manifolds equipped with a quarter-symmetric non-metric connection. It is proved that the LP-Sasakian manifold endowed with a quarter-symmetric non-metric connection is partially Ricci semisymmetric with respect to the quarter-symmetric non-metric connection if and only if it is an η-Einstein ma...

The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold endowed with a non-symmetric non-metric is irregular.

The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold endowed with a non-symmetric non-metric is irregular.

We define a new type of quarter-symmetric non-metric \xi-connection on an LP-Sasakian manifold and prove its existence. We provide its application in the general theory of relativity. To validate the existence of the quarter-symmetric non-metric \xi-connection on an LP-Sasakian manifold, we give a non-trivial example in dimension 4 and verify our r...

The fluid space-times carrying a W1-curvature tensor are studied. It is proved that the energy momentum tensor of the space-time is of Codazzi type if and only if the W1-curvature tensor is divergence free. We also show that the pseudo Ricci symmetric space-time with divergence free W1-curvature tensor is a GRW space-time. A necessary and sufficien...

In this paper, we study almost α-cosymplectic manifolds with M −projective curvature tensor and we obtain the relation between different curvature tensors.

The object of the present paper is to prove that in a quasi-
Sasakian 3-manifold admitting �-Ricci soliton, the structure function � is a
constant. As a consequence we obtain several important results.

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the con-circular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and...

We define a new type of semi-symmetric non-metric connection
on a Riemannian manifold and establish its existence. It is proved that such
connection on a Riemannian manifold is projectively invariant under certain
condition. We also find many basic results of the Riemannian manifolds and
study the properties of group manifolds and submanifolds of t...

The object of the present paper is to study the properties of Ricci
and Yamabe solitons on the perfect fluid LP-Sasakian spacetimes. Certain results related to the application of such spacetimes in the general relativity and
cosmology are obtained.

The object of the present paper is to study the properties of generalized Sasakian-space-forms. We prove the results related to Ricci symmetric, Ricci recurrent, cyclic parallel and Codazzi type Ricci tensors. Results on Ricci soliton and gradient Ricci soliton are proved. Also, we provide the examples of generalized Sasakian-space-forms which are...

The object of the present paper is to carry out η-Ricci soliton on 3-dimensional regular f-Kenmotsu manifold and we turn up some geometrical results. Furthermore we bring out the curvature conditions for which η-Ricci soliton on such manifolds are shrinking, steady or expanding. We wind up by considering examples of existence of shrinking and expan...

In this paper, we consider an η-Ricci soliton on the (LCS)n-manifolds (M, φ, ξ, η, g) satisfying certain curvature conditions likes: R(ξ, X) · S = 0 and W2(ξ, X) · S = 0. We show that on the (LCS)n-manifolds (M, φ, ξ, η, g), the existence of η-Ricci soliton implies that (M, g) is a quasi-Einstein. Further, we discuss the existence of Ricci solitons...

We set a definition of a {(0,2)} -type tensor on the generalized Sasakian-space-forms. The necessary and sufficient conditions for W -semisymmetric generalized Sasakian-space forms are studied. Certain results of the Ricci solitons, the Killing vector fields and the closed 1-form on the generalized Sasakian-space-forms are derived. We also verify o...

The object of the present paper is to study the properties of N(k)-quasi Einstein manifolds.The existence of some classes of such manifolds are proved by constructing physical and geometrical examples. It is also shown that the characteristic vector ﬁeld of the manifold is a unit parallel vector ﬁeld as well as Killing vector ﬁeld.

The present paper deals with the trans-Sasakian manifold admitting an m-projective curvature tensor. In the last, the properties of special weakly Riccisymmetricand generalized Ricci-recurrent trans-Sasakian manifolds have been studied.

This paper deals with the study of a special class of almost contact
metric manifold, called trans-Sasakian manifold. We also study the
properties of the Ricci solitons in generalized recurrent, Weyl semisymmetric,
Einstein semisymmetric, Weyl pseudo symmetric and partially Ricci
pseudo symmetric trans-Sasakian manifolds. Example of trans-Sasakian...

The object of the present paper is to study some classes of N(k)-quasi
Einstein manifolds. The existence of such manifolds are proved by giving non-trivial physical and geometrical examples. It is also proved that the characteristic vector field of the manifold is Killing as well as parallel unit vector field under certain curvature restrictions.

The present paper deals with the study of Kenmotsu manifolds equipped with a semi-symmetric metric connection. The properties of η−parallel Ricci tensor, globally symmetric and φ −symmetric Kenmotsu manifolds with the semi-symmetric metric connection are evaluated. In the end, we construct an example of a 3−dimensional Kenmotsu manifold admitting s...

The aim of the present paper is to study the Eisenhart problems
of finding the properties of second order parallel tensors (symmetric
and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate
the properties of Ricci solitons, Ricci semisymmetric, locally φsymmetric,
η-parallel Ricci tensor and a non-null concircular vector field
on (...

The present paper deals with the study of Ricci soliton on weak symmetries of almost Kenmotsu (κ, µ, ν)−space and its geometric properties. Also, we obtain the condition for Ricci soliton on weakly symmetric and weakly Ricci symmetric almost Kenmotsu (κ, µ, ν)−space with the tensor field £ ξ g + 2S is parallel to be shrinking, steady and expanding...

Trans-Sasakian manifolds with respect to a non-symmetric non-metric connection are studied. Some properties of the curvature tensor, the conformal curvature tensor, the con-harmonic curvature tensor of trans-Sasakian manifolds admitting a non-symmetric non-metric connection are studied. Nijenhuis tensor studied as well.

The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.

H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection
on a Riemannian manifold in (1932). Agashe and Cha
e [1] de�ned and studied
semi-symmetric non-metric connection on a Riemannian manifold. In the present
paper, we de�ne a new type of semi-symmetric non-metric connexion in an almost
contact metric manifold and studied its...

The aim of the present paper is to study the properties of pseudo Ricci symmetric
quasi Einstein and N(k)−quasi Einstein manifolds. We construct some examples
of N(k)−quasi Einstein manifolds which support the existence of such manifolds.

The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.

In the context of para-contact Hausdorff geometry η-Ricci solitons and gradient Ricci solitons are considered on manifolds. We establish that on an (LCS)n-manifold (M, ϕ, ξ, η, 𝑔), the existence of an ηRicci soliton implies that (M, 𝑔) is quasi-Einstein. We find conditions for Ricci solitons on an (LCS)n-manifold (M, ϕ, ξ, η, 𝑔) to be shrinking, st...

The aim of the present paper is to study the properties of generalized ϕ−recurrent and concircular ϕ−recurrent Kenmotsu manifolds.

The aim of the present paper is to study the properties of generalized φ−recurrent and concircular φ−recurrent Kenmotsu manifolds.

Recently S. K. Chaubey and R. H. Ojha [Tensor New Ser. 70, No. 2, 202–213 (2008; Zbl 1193.53035)] introduced a semi-symmetric non-metric connection in almost contact metric manifold. The purpose of the present paper is to study this connection in a Sasakian manifold. We have also studied curvature tensors of a semi-symmetric non-metric T-connection...

In this paper, some properties of m−projective curvature tensor in Kenmotsu manifolds are studied.

In this paper, some properties of m-projective curvature tensor in Kenmotsu manifolds are studied.

The present paper deals with the study of weakly m-projectively symmetric and m-projectively flat weakly Ricci-symmetric manifolds. In the end, examples of (WMPS)n and (WRS)n are given.

Yano [10] defined and studied semi-symmetric metric connection in a Riemannian manifold and this was extended by De and Senguta [4] and many other geometers. Recently, the present authors [2], [3] defined semi-symmetric non-metric connections in an almost contact metric manifold. In this paper, we studied some properties of a semi-symmetric non-met...

In this paper, some properties of m−projective curvature tensor
in Kenmotsu manifolds are studied.

In the present paper we studied the properties of the m−projective
curvature tensor in LP-Sasakian, Einstein LP-Sasakian and η−Einstein LPSasakian
manifolds.

In 1924, Friedmann and Schouten have introduced the idea of semi-symmetric linear connexion in a differentiable manifold. In 1970, semi-symmetric connexions were studied by K. Yano in a Riemannian manifold. In 2008, S. K. Chaubey and R. H. Ojha defined a new semi-symmetric non metric and quarter symmetric metric connexion. The purpose of the presen...

In this paper, we study the properties of the M −projective curvature tensor in Riemannian and Kenmotsu manifolds. M.S.C. 2000: 53D10, 53D15. Key words: Riemannian manifold; Kenmotsu manifold; M −projective curvature tensor; η−Einstein manifold and irrotational M −projective curvature tensor.

In the present paper, we studied the properties of a quarter-symmetric non-metric connection in a Kähler manifold.

In the present paper, we studied the properties of semi-symmetric non-metric connection in genralised co-symplectic manifold.

In present paper, we studied the properties of semi-symmetric metric T −connection in almost contact metric manifolds. It has been shown that a generalised co-symplectic manifold with semi-symmetric metric T −connection is a generalised quasi-Sasakian manifold. Further, an almost contact metric manifold equipped with semi-symmetric metric T −connec...