Showing papers by "Uday Chand De published in 2020"
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 metric of a (κ,μ)-almost co-Kahler manifold M2n+1 is a gradieness of a quasi-Yamabe solitons.
Abstract: We characterize almost co-Kahler manifolds with gradient Yamabe, gradient Einstein and quasi-Yamabe solitons. It is proved that if the metric of a (κ,μ)-almost co-Kahler manifold M2n+1 is a gradien...
19 citations
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.
11 citations
TL;DR: In this article, it was shown that if a contact metric manifold admits a quasi-Yamabe soliton whose soliton field is the V-Ric vector field, then the Ricci operator Q commutes with the (1, 1) tensor.
Abstract: We prove that a contact metric manifold does not admit a proper quasi-Yamabe soliton ($$M,\, g,\,\xi ,\,\lambda ,\,\mu $$). Next we prove that if a contact metric manifold admits a quasi-Yamabe soliton ($$M,\, g,\, V,\, \lambda ,\, \mu $$) whose soliton field is pointwise collinear with the Reeb vector field, then the scalar curvature is constant, and the quasi-Yamabe soliton reduces to Yamabe soliton. Finally, it is shown that if a contact metric manifold admits a quasi-Yamabe soliton whose soliton field is the V-Ric vector field, then the Ricci operator Q commutes with the (1, 1) tensor $$\phi $$. As a consequence of the main result we obtain several corollaries.
9 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 article, a necessary and sufficient condition for a spacetime with pseudo symmetric energy-momentum tensor to be a pseudo Ricci symmetric spacetime was given, and several interesting results were obtained.
9 citations
TL;DR: In this paper, the Fischer-Marsden conjecture on almost Kenmotsu manifolds was investigated and it was shown that if a 3-dimensional non-Kenmotu (k, µ) manifold is a 2-dimensional almost Kenmotu manifold, then it is possible to construct a 3D almost-Kenmotu (1, µ)-manifold.
Abstract: The purpose of this paper is to investigate the Fischer-Marsden conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional non-Kenmotsu (k, µ)′-almost Kenmotsu manifold sa...
8 citations
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TL;DR: In this paper, it was shown that if the metric of a non-cosymplectic normal almost contact metric manifold is Riemann soliton with divergence-free potential vector field (Z), then the manifold is quasi-Sakian and is of constant sectional curvature -$\lambda.
Abstract: The quest of the offering article is to investigate \emph{almost Riemann soliton} and \emph{gradient almost Riemann soliton} in a non-cosymplectic normal almost contact metric manifold $M^3$. Before all else, it is proved that if the metric of $M^3$ is Riemann soliton with divergence-free potential vector field $Z$, then the manifold is quasi-Sasakian and is of constant sectional curvature -$\lambda$, provided $\alpha,\beta =$ constant. Other than this, it is shown that if the metric of $M^3$ is \emph{ARS} and $Z$ is pointwise collinear with $\xi $ and has constant divergence, then $Z$ is a constant multiple of $\xi $ and the \emph{ARS} reduces to a Riemann soliton, provided $\alpha,\;\beta =$constant. Additionally, it is established that if $M^3$ with $\alpha,\; \beta =$ constant admits a gradient \emph{ARS} $(\gamma,\xi,\lambda)$, then the manifold is either quasi-Sasakian or is of constant sectional curvature $-(\alpha^2-\beta^2)$. At long last, we develop an example of $M^3$ conceding a Riemann soliton.
7 citations
TL;DR: In this paper, the authors investigated the almost quasi-Yamabe soliton and gradient almost quasi Yamabe solitons under the framework of three-dimensional normal almost paracontact metr...
Abstract: The purpose of the present paper is to investigate the almost quasi- Yamabe soliton and gradient almost quasi-Yamabe solitons under the framework of three-dimensional normal almost paracontact metr...
6 citations
TL;DR: In this paper, the authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a p-SASAKian manifold.
Abstract: The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition $$\tilde Z(\xi ,Y) \cdot \tilde S = 0$$, where $$\tilde Z, \tilde S$$ are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.
TL;DR: In this article, it was shown that in a 3D compact orientable cosymplectic manifold M^3 without boundary, an almost Ricci soliton reduces to Ricci s soliton under certain restriction on the potential function lambda.
Abstract: In the present paper we study three dimensional cosymplectic manifolds admitting almost Ricci solitons. Among others we prove that in a three dimensional compact orientable cosymplectic manifold M^3 withoutboundary an almost Ricci soliton reduces to Ricci soliton under certain restriction on the potential function lambda. As a consequence we obtain several corollaries. Moreover we study gradient almost Ricci solitons.
TL;DR: In this article, the authors consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms and find the necessary and sufficient conditions for Legendre curve interpolation.
Abstract: We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating se...
TL;DR: In this article, the authors studied the critical point equation conjecture on almost Kenmotsu manifolds and proved that if a three-dimensional almost-k,\mu)-manifold satisfies the conjecture, then the manifold is either locally isometric to the product space or is a kinematic manifold.
Abstract: We study the critical point equation $(CPE)$ conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional $(k,\mu)'$-almost Kenmotsu manifold satisfies the $CPE,$ then the manifold is either locally isometric to the product space $\mathbb H^2(-4)\times\mathbb R$ or the manifold is Kenmotsu manifold. Further, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the $CPE$ conjecture, then the manifold is Einstein.
TL;DR: In this paper, the effects of concircular flatness and symmetry of a warped product manifold on its fiber and base manifolds are investigated, and the divergence-free concircularity curvature tensor on warped product manifolds is considered.
Abstract: This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fiber and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence-free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson–Walker and standard static space-times.
TL;DR: In this paper, it was shown that Bach flat (k, μ) almost co-Kähler manifold is K-almost co-k-Köhler manifold with divergence free Cotton tensor.
Abstract: The object of the present paper is to characterize Bach flat (k, μ)-almost co-Kähler manifolds. It is proved that a Bach flat (k, μ)almost co-Kähler manifold is K-almost co-Kähler manifold under certain restriction on μ and k. We also characterize (k, μ)-almost co-Kähler manifolds with divergence free Cotton tensor.
TL;DR: In this article, it was shown that if a 3D para-Sasakian manifold admits gradient almost Ricci soliton under certain conditions then either the manifold is of constant sectional curvature $-1$ or it reduces to a gradient Ricci Soliton.
Abstract: The object of the offering exposition is to study almost Ricci soliton and gradient almost Ricci soliton in 3-dimensional para-Sasakian manifolds. At first, it is shown that if $(g, V,\lambda)$ be an almost Ricci soliton on a 3-dimensional para-Sasakian manifold $M$, then it reduces to a Ricci soliton and the soliton is expanding for $\lambda$=-2. Besides these, in this section, we prove that if $V$ is pointwise collinear with $\xi$, then $V$ is a constant multiple of $\xi$ and the manifold is of constant sectional curvature $-1$. Moreover, it is proved that if a 3-dimensional para-Sasakian manifold admits gradient almost Ricci soliton under certain conditions then either the manifold is of constant sectional curvature $-1$ or it reduces to a gradient Ricci soliton. Finally, we consider an example to justify some results of our paper.