Characterization of three-dimensional Riemannian manifolds with a type of semi-symmetric metric connection admitting Yamabe soliton
TL;DR: In this article, it was shown that a 3D Riemannian manifold endowed with a semi-symmetric ρ-connection, whose metric is a Yamabe soliton, is a manifold of constant sectional curvature − 1 and the soliton is expanding with soliton constant − 6.
About: This article is published in Journal of Geometry and Physics.The article was published on 2020-11-01. It has received 11 citations till now. The article focuses on the topics: Riemannian manifold & Metric connection.
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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 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 paper, the authors characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.
Abstract: In this paper, we characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.
11 citations
TL;DR: In this article, a three-dimensional N(k)-contact metric manifold M admits a Yamabe soliton of type (M,g,V ), and the manifold has a constant scalar curvature and the flow vector field V is Killing.
Abstract: If a three-dimensional N(k)-contact metric manifold M admits a Yamabe soliton of type (M,g,V ), then the manifold has a constant scalar curvature and the flow vector field V is Killing. Furthermore...
9 citations
TL;DR: In this paper , the authors characterized the geodesically complete Lorentzian manifolds equipped with a semi-symmetric non-metric ρ-connection and established the conditions for such a manifold to be a generalized Robertson-Walker spacetime.
Abstract: The focus of this paper is to characterize the Lorentzian manifolds equipped with a semi-symmetric non-metric ρ-connection [briefly, [Formula: see text]]. 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 [Formula: see text] is geodesically complete. We also study the properties of almost Ricci solitons and gradient almost Ricci solitons on Lorentzian manifolds and Yang pure space, respectively. Finally, we study the properties of semisymmetric [Formula: see text], and it is proven that [Formula: see text] is semisymmetric if and only if it is a Robertson–Walker spacetime.
6 citations
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Journal Article•
TL;DR: In this article, the authors study the property of D-conharmonic transformation and obtain that the identity transformation is actually the identity transform, which is the transformation of the D-ConHarmonic transformation.
Abstract: We study the property of D-conharmonic transformation and obtain that the D-conharmonic transformation is actually the identity transformation.
189 citations
138 citations