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June 2018 - October 2020

August 2017 - May 2018

## Publications

Publications (12)

A submanifold Mn of a Euclidean space EN is called biharmonic if ΔH→=0, where H→ is the mean curvature vector of Mn. A well known conjecture of B.Y. Chen states that the only biharmonic submanifolds of Euclidean spaces are the minimal ones. Ideal submanifolds were introduced by Chen as those which receive the least possible tension at each point. I...

A submanifold $M^n$ of a Euclidean space $\mathbb{E}^N$ is called biharmonic if $\Delta\vec{H}=0$, where $\vec{H}$ is the mean curvature vector of $M^n$. A well known conjecture of B.Y. Chen states that the only biharmonic submanifolds of Euclidean spaces are the minimal ones. Ideal submanifolds were introduced by Chen as those which receive the le...

Lorentz hypersurfaces \(M_{1}^{4}\) is studied in \(E_{1}^{5}\) with non-diagonal shape operators having characteristic equation \((y-\lambda )^2(y-\lambda _3)(y-\lambda _4)\) or \((y-\lambda )^3(y-\lambda _4)\) or \(((y-\lambda )^2+\mu ^2)(y-\lambda _3)(y-\lambda _4)\). It is proved that if the mean curvature vector field \(\vec {H}\) of Lorentz h...

Ideal submanifolds are submanifolds which receive the least possible tension from its ambient space and have many interesting applications in several areas of mathematics. In this paper, we have investigated null 2-type \(\delta (r)\)-ideal hypersurfaces for every integer \(r \in [2, n-1]\) in Euclidean space \(\mathbb {E}^{n+1} (n > 2)\) with an e...

A biconservative submanifold of a Riemannian manifold is a sub-manifold with divergence free stress-energy tensor with respect to bienergy. These are generalizations of biharamonic submanifolds. In 2013, B.Y. Chen and M.I. Munteanu proved that δ(2)-ideal and δ(3)-ideal biharmonic hypersurfaces in Euclidean space are minimal. In this paper, we gener...

We study Lorentz hypersurfaces $M_{1}^{n}$ in $E_{1}^{n+1}$ satisfying $\triangle \vec {H}= \alpha \vec {H}$ with non diagonal shape operator, having complex eigenvalues. We prove that every such Lorentz hypersurface in $E_{1}^{n+1}$ having at most five distinct principal curvatures has constant mean curvature.

In this paper, we obtain some properties of biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex eigen values. We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with at most five distinct principal curvatures has constant...

In this paper, we obtain that every biharmonic non-degenerate hypersurfaces in semi-Euclidean space E5s with constant scalar curvature of diagonal shape operator has zero mean curvature.

We prove that every biharmonic hypersurface having constant higher order mean curvature Hr for r > 2 in a space form M⁵(c) is of constant mean curvature. In particular, every such biharmonic hypersurface in 𝕊⁵(1) has constant mean curvature. There exist no such compact proper biharmonic isoparametric hypersurfaces M in 𝕊⁵(1) with four distinct prin...

In this paper, we study Lorentz hypersurface Mn1 in En+11 satisfying △⃗H = α⃗H with minimal polynomial [(y−λ)2+μ2](y−λ1)(y−λn) having shape operator (2.11). We prove that every such Lorentz hypersurface in En+11 having at most four distinct principal curvatures has constant mean curvature.

We prove non-existence of proper biharmonic hypersurfaces of zero scalar curvature in Euclidean space E5.