# Sabina Eyasmin's research while affiliated with Jadavpur University and other places

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## Publications (18)

The Morris-Thorne wormhole is a spherically symmetric solution of Einstein field equations with cosmological constant. The present article aims to investigate the geometric properties in terms of curvatures admitted by this spacetime. It is found that such a spacetime possesses several kinds of symmetries, such as, Ricci generalized pseudosymmetry,...

Generalized quasi-conformal curvature tensor (ω-tensor) has the flavour of conformal, conharmonic, concircular, projective, m-projective, W1-curvature, W2-curvature and W4-curvature tensors. In the present paper we have investigated the nature of Riemann solitons in α-cosymplectic manifold in the light of generalized weakly ω-symmetric structure.

The objective, in this paper, is to obtain the curvature properties of (t−z)-type plane wave metric studied by Bondi et al. (1959). For this a general (t−z)-type wave metric is considered and the condition for which it obeys Einstein’s empty spacetime field equations is obtained. It is found that the rank of the Ricci tensor of (t−z)-type plane wav...

The hypersurface of a space is one of the most important objects in a space. Many authors studied the various geometric aspects of hypersurfaces in a space form. The notion of conformal flatness is one of the most primitive concepts in differential geometry. Again, conformally flat space is a proper generalization of a space form. In this paper, we...

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geod...

(CS)4-spacetimes with Einstein field equations under some curvature restriction named
generalized weakly Ricci-symmetry have been studied. We have proved that if the characteristic
vector field ξ of a generalized weakly Ricci-symmetric (CS)4-spacetime obeying
Einstein equation is a Killing vector field, then such a spacetime admits (i) curvature
co...

The object of the present paper is to study the Ken-motsu manifolds which metric tensor is η-Ricci soliton. We bring out curvature conditions for which Ricci solitons in Kenmotsu man-ifolds are sometimes shrinking or expanding and some other times steady.

This paper ensure the existence of weakly Ricci symmetric Riemannian manifolds admitting a semi-symmetric metric connection by several non-trivial examples.

The object of the present paper is to study a transformation called D-homothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor ϕ and the operator Qϕ − ϕQ is conformal under a D-homothetic deformation. Also the ϕ-sectional curvature...

The object of the present paper is to provide the existence of LP-Sasakian manifolds with -recurrent, -parallel, -recurrent, -parallel Ricci tensor with several non-trivial examples. Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples.

The object of the present paper is to provide the existence of φ-recurrent (LCS) n -manifolds with several non-trivial examples. Key words: (LCS) n -manifold, locally φ-recurrent, 1-form, manifold of constant curvature, scalar curvature. AMS Subject Class. (2000): 53C15, 53C25.

The object of the present paper is to study a transformation called D-homothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor φ and the operator Qφ - φQ is conformai under a D-homothetic deformation. Also the φ-sectional curvature...

The object of the present paper is to introduce a type of non-flat Riemannian manifold called weakly pseudo quasi-conformally symmetric manifold and proved its existence by several non-trivial examples and also obtained many interesting results.

The object of the present paper is to provide the existence of Á-recurrent (LCS)n- manifolds with several non-trivial examples.

The aim of the present paper is to introduce a type of contact metric manifolds called φ-recurrent generalized (k, μ)-contact metric manifolds and to study their geometric properties. The existence of such manifolds is ensured by a non-trivial example.

The object of the present paper is to study locally ϕ-symmetric (LCS) n manifolds with several non-trivial examples.

## Citations

... Also if α = 0, then the m-quasi-Einstein manifold turns into a Ricci simple manifold. We note that Morris-Thorne spacetime [103] and Gödel spacetime [28] are Ricci simple manifolds, Robertson-Walker spacetime [26] and Siklos spacetime [29] are quasi-Einstein manifolds, Kantowski-Sachs spacetime [84] and Som-Raychaudhuri spacetime [25] are 2-quasi Einstein manifolds and Kaigorodov spacetime [29] is an Einstein manifold. For curvature properties of Robinson-Trautman metric, Melvin magnetic metric and generalized pp-wave metric, etc., we refer the reader to see [30,[104][105][106]. ...

... A large number of such works are taken over semi-Euclidean ambient space, i.e., see [4], [25], [14], [12], [13], [22], [24], [29] , [30], [43] and references therein. Conformally flat space is a natural generalization of semi-Euclidean space and in literature we found some works on hypersurfaces embedded in conformally flat space, e.g., see [27], [24], [28], [30] and references therein. In this paper we study some geometric properties of hypersurfaces in conformally flat ambient space. ...

... We note that Morris-Thorne spacetime [103] and Gödel spacetime [28] are Ricci simple manifolds, Robertson-Walker spacetime [26] and Siklos spacetime [29] are quasi-Einstein manifolds, Kantowski-Sachs spacetime [84] and Som-Raychaudhuri spacetime [25] are 2-quasi Einstein manifolds and Kaigorodov spacetime [29] is an Einstein manifold. For curvature properties of Robinson-Trautman metric, Melvin magnetic metric and generalized pp-wave metric, etc., we refer the reader to see [30,[104][105][106]. ...

... for any vector fields X , Y , Z on M n . It is to be noted that for n = 4, such space is known as (C S) 4 -space ( [4,5]). ...

... We also highlighted that example of all such classes exist on different types of almost contact metric manifold. The notion of η-Ricci almost solitons have been studied by many authors on different types of almost contact metric manifolds (see [5,9,15,26,29]). For instance, it has been studied for Hopf hypersurfaces in complex space forms in [9], for the Lorentzian para-Sasakian manifold in [5], for the para-Sasakian manifold in [26] and for the Kenmotsu manifold in [29]. ...

... 674PRABHAVATI G. ANGADI, G.S. SHIVAPRASANNA, G. SOMASHEKHARA, P.S.K. REDDY then from (5) and (7) we have (8) ...

... LP-Sasakian manifolds introduced by Matsumoto [8] is generalized by Shaikh [13] by introducing the notion of Lorentzian concircular structure manifolds (briefly, (LCS) n −manifolds). Many geometers studied (LCS) n -manifold since it has been first introduced (see, for details, [1,12,14,15,16]). ...

... In 1989 Tamássy and Binh [36] generalized the Chaki's notion of pseudosymmetry and introduced the notion of weakly symmetric manifold. We note that Shaikh and his co-authors ( [12], [21]- [25]) studied this notion of weak symmetry with various generalized curvature tensors. Again generalizing the results of Binh [2], recently, Shaikh and Kundu [26] obtained the characterization of warped product weakly symmetric manifold. ...

... In view of (2), (20), (21), (22) and (23), we havẽ ...

... Cartan noticed that all locally symmetric and 2-dimensional Riemannian spaces belong to a class of Riemannian manifold satisfying the condition R(U, V ) · R = 0. Kowalski [9] studied 3-dimensional Riemannian manifold satisfying R(U, V ) · R = 0. In recent years, many geometers [10][11][12][13][14][15] studied (k, µ)-contact metric manifolds, as it is an interesting topic in differential geometry. One of its interesting characteristics is that there is a special case of (k, µ)-spaces which were the first known example of a non-sasakian locally φ-symmetric space [16]. ...