Author
S. K. Chaubey
Bio: S. K. Chaubey is an academic researcher from Higher College of Technology. The author has contributed to research in topics: Mathematics & Pure mathematics. The author has an hindex of 6, co-authored 21 publications receiving 109 citations.
Topics: Mathematics, Pure mathematics, Manifold, Metric connection, Einstein
Papers
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01 Jan 2010
TL;DR: In this paper, the curvature tensors of a semisymmetric non-metric T−connection in an almost contact metric manifold were studied and the purpose of the present paper is to study this connection in a Sasakian manifold.
Abstract: Recently S. K. Chaubey and R. H. Ojha [1] introduced a semisymmetric 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 semisymmetric non-metric T−connection in an almost contact metric manifold.
35 citations
TL;DR: In this paper, it was shown that the Weyl tensor is divergence-free and the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime.
Abstract: 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 are geodesics. Moreover, it is shown that in a generalized Robertson–Walker perfect fluid spacetime, the Weyl tensor is divergence-free and the gradient of the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime. We also characterize the perfect fluid spacetimes whose Lorentzian metrics are Yamabe and gradient Yamabe solitons, respectively.
22 citations
TL;DR: In this article , Chen's inequalities involving Chen's δ-invariant δM, 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 are derived.
Abstract: 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 obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.
16 citations
01 Jan 2010
TL;DR: In this article, the authors studied the properties of semi-symmetric metric T −connection in almost contact metric manifolds, and showed that a generalised co-symplectic manifold equipped with T −connections is a quasi-Sasakian manifold if and only if it is locally isometric to H n (−1).
Abstract: 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 −connection is either projectively or con-circularly flat if and only if it is locally isometric to the hyperbolic space H n (−1).
15 citations
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TL;DR: In this paper, the authors provide a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students, covering Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.
Abstract: Hans Stephani 1982 Cambridge: Cambridge University Press xvi + 298 pp price £25 This textbook provides a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students. It covers Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.
78 citations
TL;DR: In this paper, it was proved that a Lorentzian manifold endowed with a semi-symmetric metric connection is a GRW spacetime and characterized the Ricci semisymmetric manifold.
Abstract: 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 $$\rho $$
-connection is a GRW spacetime. We also characterize the Ricci semisymmetric Lorentzian manifold and study the solution of Eisenhart problem of finding the second order parallel (skew-)symmetric tensor on Lorentzian manifolds. Finally, we address physical interpretation of some geometric results of our paper.
28 citations
TL;DR: In this article , the authors investigated the differential geometric characteristics of pedal and primitive curves in a Minkowski plane, where a primitive is specified by the opposite structure for creating the pedal, and primitivoids are known as comparatives of the primitive of a plane curve.
Abstract: In this work, we investigate the differential geometric characteristics of pedal and primitive curves in a Minkowski plane. A primitive is specified by the opposite structure for creating the pedal, and primitivoids are known as comparatives of the primitive of a plane curve. We inspect the relevance between primitivoids and pedals of plane curves that relate with symmetry properties. Furthermore, under the viewpoint of symmetry, we expand these notions to the frontal curves in the Minkowski plane. Then, we present the relationships and properties of the frontal curves in this category. Numerical examples are presented here in support of our main results.
24 citations