scholarly journals Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 179-186
Author(s):  
Sharief Deshmukh ◽  
Uday De ◽  
Peibiao Zhao
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field ? belonging to the (k,?)'-nullity distribution and (k,?)-nullity distribution respectively. Finally, an illustrative example is given.

scholarly journals On almost Kenmotsu manifolds with nullity distributions

2017 ◽  
Vol 48 (3) ◽  
pp. 251-262 ◽  
Author(s):  
Uday Chand De ◽  
Jae Bok Jun ◽  
Krishanu Mandal
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Characteristic Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Projective Curvature ◽  
Nullity Distribution ◽  
Projective Curvature Tensor ◽  
Characteristic Vector Field

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.

scholarly journals On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

2018 ◽  
Vol 33 (2) ◽  
pp. 255
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Conformally Flat ◽  
Kenmotsu Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with  $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

scholarly journals Certain results on N(k)-contact metric manifolds

2018 ◽  
Vol 49 (3) ◽  
pp. 205-220
Author(s):  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Characteristic Vector ◽  
Ricci Solitons ◽  
Gradient Ricci Solitons ◽  
Contact Metric Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

In the present paper we study contact metric manifolds whose characteristic vector field $\xi$ belonging to the $k$-nullity distribution. First we consider concircularly pseudosymmetric $N(k)$-contact metric manifolds of dimension $(2n+1)$. Beside these, we consider Ricci solitons and gradient Ricci solitons on three dimensional $N(k)$-contact metric manifolds. As a consequence we obtain several results. Finally, an example is given.

scholarly journals ∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

2019 ◽  
Vol 69 (6) ◽  
pp. 1447-1458 ◽  
Author(s):  
Venkatesha ◽  
Devaraja Mallesha Naik ◽  
H. Aruna Kumara
Keyword(s):  
Vector Field ◽  
Ricci Soliton ◽  
Characteristic Vector ◽  
Ricci Solitons ◽  
Potential Vector ◽  
Open Set ◽  
Kenmotsu Manifolds ◽  
Almost Ricci Soliton ◽  
Characteristic Vector Field ◽  
Potential Vector Field

Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.

scholarly journals On Generalized ϕ-Recurrent (ϵ,δ)-Trans-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
C. S. Bagewadi ◽  
Dakshayani A. Patil
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Characteristic Vector ◽  
Sasakian Manifolds ◽  
Characteristic Vector Field

We study generalized ϕ-recurrent (ϵ,δ)-trans-Sasakian manifolds. A relation between the associated 1-forms A and B and relation between characteristic vector field ξ and the vector fields ρ1, ρ2 for a generalized ϕ-recurrent.

scholarly journals *-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

2019 ◽  
Vol 17 (1) ◽  
pp. 874-882 ◽  
Author(s):  
Xinxin Dai ◽  
Yan Zhao ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Ricci Soliton ◽  
Contact Transformation ◽  
Kenmotsu Manifold ◽  
Potential Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Dimension 2 ◽  
Potential Vector Field

Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

scholarly journals Second order parallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 839-847 ◽  
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Second Order ◽  
Dimensional Manifold ◽  
Kenmotsu Manifold ◽  
Metric Tensor ◽  
Riemannian Product ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Order Parallel

In this paper, we prove that if there exists a second order symmetric parallel tensor on an almost Kenmotsu manifold (M2n+1, ?, ?, ?, g) whose characteristic vector field ? belongs to the (k,?)'-nullity distribution, then either M2n+1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, or the second order parallel tensor is a constant multiple of the associated metric tensor of M2n+1. Furthermore, some properties of an almost Kenmotsu manifold admitting a second order parallel tensor with ? belonging to the (k,?)-nullity distribution are also obtained.

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