Showing papers by "Uday Chand De published in 2012"

On Conformally Flat Almost Pseudo-Ricci Symmetric Spacetimes

Abstract: We consider a conformally flat almost pseudo-Ricci symmetric spacetime. At first we show that a conformally flat almost pseudo-Ricci symmetric spacetime can be taken as a model of the perfect fluid spacetime in general relativity and cosmology. Next we show that if in a conformally flat almost pseudo-Ricci symmetric spacetime the matter distribution is perfect fluid whose velocity vector is the vector field corresponding to 1-form B of the spacetime, the energy density and the isotropic pressure are not constants. We also show that a conformally flat almost pseudo-Ricci symmetric spacetime is the Robertson-Walker spacetime. Finally we give an example of a conformally flat almost pseudo-Ricci symmetric spacetime with non-zero non-constant scalar curvature admitting a concircular vector field.

Some curvature properties of generalized Sasakian-space-forms

Abstract: The object of the present paper is to study generalized Sasakian-space-forms with vanishing quasi-conformal curvature tensor. The space-forms satisfying ▿S = 0 and R.S = 0 are also considered.

Some Results on Generalized Sasakian-Space-Forms

Abstract: The object of the present paper is to study locally - symmetric generalized Sasakian-space-forms and generalized Sasakian-space-forms with - recurrent Ricci tensor. Such space-forms with three-dimensional quasi-Sasakian structure are also considered.

On almost pseudo concircularly symmetric manifolds

Abstract: The object of the present paper is to study a type of non-flat Riemannian manifold called almost pseudo concircularly symmetric manifold. The existence of an almost pseudo concircularly symmetric manifold is also shown by two non-trivial examples.

On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity

Abstract: The object of the present paper is to study almost pseudo-conformally symmetric Ricci-recurrent manifolds. The existence of almost pseudo-conformally symmetric Ricci-recurrent manifolds has been proved by an explicit example. Some geometric properties have been studied. Among others we prove that in such a manifold the vector field ϱ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field ϱ are geodesic. We also study some global properties of such a manifold. Finally, we study almost pseudo-conformally symmetric Ricci-recurrent spacetime. We obtain the Segre’ characteristic of such a spacetime.

On a class of three-dimensional trans-sasakian manifolds

Abstract: The object of the present paper is to study 3-dimensional trans-Sasakian manifolds with conservative curvature tensor and also 3-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected -Einstein 3-dimensional trans-Sasakian manifolds. Finally, an example of a 3-dimensional trans-Sasakian manifold is given, which verifies our results.

A CLASSIFICATION OF (κ, μ)-CONTACT METRIC MANIFOLDS

Abstract: In this paper we study h-projectively semisymmetric, φ-projectively semisymmetric, h-Weyl semisymmetric and φ-Weyl semisymmetric non-Sasakian (k, μ)-contact metric manifolds. In all the cases the manifold becomes an η-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian (k, μ)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N(k)-contact metric manifold.

On some Curvature Properties of K-contact Manifolds

Abstract: The object of the present paper is to study projective curvature tensor in K- contact manifolds. Projectively at and projectively semisymmetric K-contact manifolds are considered. Projectively pseudosymmetric and pseudoprojectively at K-contact manifolds are also studied. It is shown that in all the cases the K-contact manifold becomes Sasakian.

On weakly symmetric spacetimes

Abstract: In the present paper we study weakly symmetric spacetimes. The existence of such a spacetime has been proved by a non-trivial example.

On \phi-Concircularly Symmetric Kenmotsu Manifolds

Abstract: We study locally and globally \phi -concircularly symmetric Kenmotsu manifolds. At first we show that in a Kenmotsu manifold globally \phi -symmetry and globally \phi -concircularly symmetry are equivalent. Next we study 3-dimensional locally \phi -concircularly symmetric Kenmotsu manifolds. Finally, we give some examples of \phi -concircularly symmetric Kenmotsu manifolds.

Certain curvature properties of generalized Sasakian-space-forms

Abstract: The object of the present paper is to study Ricci pseudosymmetric and Weyl semisymmetric generalized Sasakian-space-forms. Quasi-umbilical hypersurfaces of generalized Sasakian-space-forms have also been studied.

On the Conharmonic Curvature Tensor of Generalized Sasakian-Space-Forms

Abstract: The object of the present paper is to characterize generalized Sasakian-space-forms satisfying certain curvature conditions on conharmonic curvature tensor. In this paper we study conharmonically semisymmetric, conharmonically flat, -conharmonically flat, and conharmonically recurrent generalized Sasakian-space-forms. Also generalized Sasakian-space-forms satisfying and have been studied.

Quarter-Symmetric Nonmetric Connection on -Sasakian Manifolds

Abstract: The object of the present paper is to study a quarter-symmetric nonmetric connection on a -Sasakian manifold. In this paper we consider the concircular curvature tensor and conformal curvature tensor on a -Sasakian manifold with respect to the quarter-symmetric nonmetric connection. Next we consider second-order parallel tensor with respect to the quarter-symmetric non-metric connection. Finally we consider submanifolds of an almost paracontact manifold with respect to a quarter-symmetric non-metric connection.

The Structure of a Class of Generalized Sasakian-Space-Forms

Abstract: The object of the present paper is to study ξ-conformally at and ϕ-conformally at generalized Sasakian-space-forms. at, ϕ-conformally at, Sasakian manifold, Einstein manifold, η-Einstein manifold, conformally at.