Showing papers by "Uday Chand De published in 2017"
TL;DR: In this paper, the authors characterized Weyl semisymmetric almost Kenmotsu manifolds with characteristic vector field ξ belonging to the ( k, μ ) − nullity distribution and ( k, μ ) -nullity distribution respectively.
11 citations
Journal Article•
TL;DR: In this article, it was shown that a Ricci soliton admits a Reeb vector field if and only if the manifold is a paraSasaki-Einstein manifold, and an illustrative example is constructed.
Abstract: The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discussed. Finally, an illustrative example is constructed.
8 citations
TL;DR: In this article, mixed quasi-Einstein manifolds have been studied and some geometric properties of mixed QE2Einstein manifold have been discussed, and M(QE)4 spacetime with spac...
Abstract: The object of the present paper is to study mixed quasi-Einstein manifolds. Some geometric properties of mixed quasi-Einstein manifolds have been studied. We also discuss M(QE)4 spacetime with spac...
6 citations
TL;DR: In this article, the Ricci pseudo-symmetric and Ricci generalized P-Sasakian manifolds were investigated and the curvature condition S R = 0 was defined.
Abstract: In this paper, we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric P-Sasakian manifolds. Next we study P-Sasakian manifolds satisfying the curvature condition S R = 0: Finally, we give an example of a 5-dimensional P-Sasakian manifold to illustrate some results.
5 citations
TL;DR: In this article, the authors studied second order symmetric parallel tensors in generalized contact metric manifolds and its applications to Ricci solitons, and proved that a generalized contact manifold admits a Ricci-soliton whose potential vector field is the Reeb vector field if and only if the manifold is a Sasaki-Einstein manifold.
Abstract: The object of the present paper is to study second order symmetric parallel tensors in generalized \((k,\,\mu )\)-contact metric manifolds and its applications to Ricci solitons. Next, we prove that a generalized \((k,\,\mu )\)-contact metric manifold M admits a Ricci soliton whose potential vector field is the Reeb vector field \(\xi \) if and only if M is a Sasaki–Einstein manifold. Finally, we give some examples of generalized \((k,\,\mu )\)-contact metric manifold.
5 citations
TL;DR: In this article, the authors investigate locally φ-conformally symmetric almost Kenmotsu manifolds with their characteristic vector field ξ belonging to some nullity distribution and they give an example of a 5-dimensional almost Ken motsu manifold such that ξ belongs to the (k, μ)′-nullity distribution.
Abstract: The aim of this paper is to investigate locally φ-conformally symmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ξ belongs to the (k, μ)′-nullity distribution and h′ 6= 0.
3 citations
TL;DR: In this article, the authors studied a conharmonically flat spacetime with cyclic parallel Ricci tensor and proved that the energy-momentum tensor is cyclic-parallel and conversely, the integral curves of the vector field U are geodesics.
Abstract: The object of the present paper is to study a spacetime admitting conharmonic curvature tensor and some geometric properties related to this spacetime. It is shown that in a conharmonically flat spacetime with cyclic parallel Ricci tensor, the energy–momentum tensor is cyclic parallel and conversely. Finally, we prove that for a radiative perfect fluid spacetime if the energy–momentum tensor satisfying the Einstein’s equations without cosmological constant is generalized recurrent, then the fluid has vanishing vorticity and the integral curves of the vector field U are geodesics.
3 citations
15 Oct 2017
TL;DR: In this paper, the Ricci tensor tensor and curvature tensor have been used to characterize generalized pseudo-symmetric and generalized (k, ε)-paracontact metric manifolds.
Abstract: In this paper we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric generalized $(k,\mu )$-paracontact metric manifolds. Besides this we characterize generalized $(k,\mu )$-paracontact metric manifolds satisfying the curvature conditions $Q(S,R)=0$ and $Q(S,g)=0$, where $S$, $R$ are the Ricci tensor and curvature tensor respectively. Several corollaries are also obtained.
2 citations
23 Sep 2017
TL;DR: In this article, it was shown that the Ricci almost soliton is not present in a metric manifold with potential Reeb vector field (RVF) whose potential vector field is a product of a flat (n+1) manifold and an n-dimensional manifold of negative constant curvature.
Abstract: The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,\mu)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,\mu)$-paracontact metric manifold $M$ with $k -1$ and whose potential vector field is the Reeb vector field $\xi$. Further, if the metric $g$ of a $(k,\mu)$-paracontact metric manifold $M^{2n+1}$ with $k
eq-1$ is a gradient Ricci almost soliton, then we prove either the manifold is locally isometric to a product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of negative constant curvature equal to $-4$, or, $M^{2n+1}$ is an Einstein manifold.
2 citations
TL;DR: In this paper, the authors characterized the curvature conditions of the Weyl projective curvature tensor and obtained several corollaries for the main results of the main result.
Abstract: The object of this paper is to characterize the curvature conditions $R\cdot P=0$ and $P\cdot S=0$ with its characteristic vector field $\xi$ belonging to the $(k,\mu)'$-nullity distribution and $(k,\mu)$-nullity distribution respectively, where $P$ is the Weyl projective curvature tensor. As a consequence of the main results we obtain several corollaries.
1 citations
TL;DR: In this article, the authors introduced a new tensor named B-tensor, which generalizes the Z tensor introduced by Mantica and Suh [Pseudo Z symmetric Riemannian manifolds with harmonic curvature tensors, Int. Geom. Phys. Methods Mod. 9(1) (2012) 1250004].
Abstract: In this paper, we introduce a new tensor named B-tensor which generalizes the Z-tensor introduced by Mantica and Suh [Pseudo Z symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. Then, we study pseudo-B-symmetric manifolds (PBS)n which generalize some known structures on pseudo-Riemannian manifolds. We provide several interesting results which generalize the results of Mantica and Suh [Pseudo Z symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. At first, we prove the existence of a (PBS)n. Next, we prove that a pseudo-Riemannian manifold is B-semisymmetric if and only if it is Ricci-semisymmetric. After this, we obtain a sufficient condition for a (PBS)n to be pseudo-Ricci symmetric in the sense of Deszcz. Also, we obtain the explicit form of the Ricci tensor in a (PBS)n if the B-tensor is of Codazzi type. Finally, we consider conformally flat pseudo-B-symmetric manifolds and prove that a (PBS)n(n > 3) spacetime is a pp-wave under certain conditions.
14 Aug 2017
TL;DR: In this paper, the authors characterize 3D almost Kenmotsu manifolds with belonging to the (k;\mu )'-nullity distribution and h'
eq 0 satisfying certain geometric conditions.
Abstract: The aim of this paper is to characterize 3-dimensional almost Kenmotsu manifolds with belonging to the (k;\mu )'-nullity distribution and h'
eq 0 satisfying certain geometric conditions. Finally, we give an example to verify some results.
TL;DR: In this article, the Ricci semisymmetric contact metric manifold is studied and the symmetric properties of a second order parallel tensor in contact metric manifolds are investigated.
Abstract: The object of the present paper is to study Ricci semisymmetric contact metric manifolds. As a consequence of the main result we deduce some important corollaries. Besides these we study contact metric manifolds satisfying the curvature condition Q.R = 0, where Q and R denote the Ricci operator and curvature tensor respectively. Also we study the symmetric properties of a second order parallel tensor in contact metric manifolds. Finally, we give an example to verify the main result.
TL;DR: In this paper, the authors studied Ricci tensors in a three dimensional generalized Sasakian space-form and showed that the Ricci solitons are semisymmetric.
Abstract: The object of the present paper is to study Ricci semisymmetric, locally $$\phi $$
-symmetric and $$\eta $$
-parallel Ricci tensor in a three dimensional generalized Sasakian-space-form. The three dimensional quasi-Sasakian generalized Sasakian-space-forms have been studied. Besides these, Ricci solitons and gradient Ricci solitons have been studied. Finally, illustrative examples are given.
TL;DR: In this paper, the Ricci semisymmetric paracontact metric manifolds with the curvature condition Q ⋅ R = 0 {Q\\cdot R=0} were studied.
Abstract: Abstract The purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying ∇ ξ h = 0 {\
abla_{\\xi}h=0} and such that the sectional curvature of the plane section containing ξ equals a non-zero constant c. Also, we study paracontact metric manifolds satisfying the curvature condition Q ⋅ R = 0 {Q\\cdot R=0} , where Q and R are the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed.