A note on invariant submanifolds of CR-integrable almost Kenmotsu manifolds

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6211-6218 ◽  
Author(s):  
Young Suh ◽  
Krishanu Mandal ◽  
Uday De
Keyword(s):  
Invariant Submanifold ◽  
Kenmotsu Manifold ◽  
Totally Geodesic ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Invariant Submanifolds

The present paper deals with invariant submanifolds of CR-integrable almost Kenmotsu manifolds. Among others it is proved that every invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold with k < -1 is totally geodesic. Finally, we construct an example of an invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold which is totally geodesic.

scholarly journals Gradient Ricci solitons on almost Kenmotsu manifolds

2015 ◽  
Vol 98 (112) ◽  
pp. 227-235 ◽  
Author(s):  
Yaning Wang ◽  
Uday De ◽  
Ximin Liu
Keyword(s):  
Ricci Soliton ◽  
Einstein Metric ◽  
Dimensional Manifold ◽  
Kenmotsu Manifold ◽  
Riemannian Product ◽  
Gradient Ricci Soliton ◽  
Almost Kenmotsu Manifold ◽  
Gradient Ricci Solitons ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds

If the metric of an almost Kenmotsu manifold with conformal Reeb foliation is a gradient Ricci soliton, then it is an Einstein metric and the Ricci soliton is expanding. Moreover, let (M2n+1,?,?,?,g) be an almost Kenmotsu manifold with ? belonging to the (k,?)?-nullity distribution and h h?0. If the metric g of M2n+1 is a gradient Ricci soliton, then M2n+1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a at n-dimensional manifold, also, the Ricci soliton is expanding with ? = 4n.

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.

scholarly journals ON f-KENMOTSU MANIFOLDS AND THEIR SUBMANIFOLDS WITH QUARTER SYMMETRIC METRIC CONNECTIONS

2021 ◽  
pp. 1017
Author(s):  
Avijit Sarkar ◽  
Nirmal Biswas
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kenmotsu Manifold ◽  
Totally Geodesic ◽  
Kenmotsu Manifolds ◽  
Invariant Submanifolds ◽  
Necessary And Sufficient

The object of the present paper is to study invariant submanifolds of f-Kenmotsu manifolds with respect to quarter symmetric metric connections. Some necessary and sufficient conditions for such submanifolds to be totally geodesic have been deduced. Also we construct an example of a submanifold of a five-dimensional f-Kenmotsu manifold to justify our results.

scholarly journals On the Classification of Almost Kenmotsu Manifolds of Dimension 3

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Classification Theorem ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Almost Kenmotsu Manifold ◽  
Geometric Conditions ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Weyl Manifold

This paper deals with the classification of a 3-dimensional almost Kenmotsu manifold satisfying certain geometric conditions. Moreover, by applying our main classification theorem, we obtain some suffcient conditions for an almost Kenmotsu manifold of dimension 3 to be an Einstein-Weyl manifold.

scholarly journals Curvature properties of almost Kenmotsu manifolds with generalized nullity conditions

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3807-3816
Author(s):  
Yaning Wang ◽  
Wenjie Wang
Keyword(s):  
Hyperbolic Space ◽  
Local Symmetry ◽  
Kenmotsu Manifold ◽  
Riemannian Product ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Weak Symmetry

In this paper, it is proved that on a generalized (k,?)'-almost Kenmotsu manifold M2n+1 of dimension 2n + 1, n > 1, the conditions of local symmetry, semi-symmetry, pseudo-symmetry and quasi weak-symmetry are equivalent and this is also equivalent to that M2n+1 is locally isometric to either the hyperbolic space H2n+1(-1) or the Riemannian product Hn+1(-4)xRn. Moreover, we also prove that a generalized (k,?)-almost Kenmotsu manifold of dimension 2n + 1, n > 1, is pseudo-symmetric if and only if it is locally isometric to the hyperbolic space H2n+1(-1).

scholarly journals Some type of semisymmetry on two classes of almost Kenmotsu manifolds

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Hyperbolic Space ◽  
Einstein Manifold ◽  
Local Symmetry ◽  
Curvature Condition ◽  
Kenmotsu Manifold ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds

Abstract The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a (k, µ)-almost Kenmotsu manifold satisfying the curvature condition Q · R = 0 is locally isometric to the hyperbolic space ℍ2 n +1(−1). Also in (k, µ)-almost Kenmotsu manifolds the following conditions: (1) local symmetry (∇R = 0), (2) semisymmetry (R·R = 0), (3) Q(S, R) = 0, (4) R·R = Q(S, R), (5) locally isometric to the hyperbolic space ℍ2 n +1(−1) are equivalent. Further, it is proved that a (k, µ)′ -almost Kenmotsu manifold satisfying Q · R = 0 is locally isometric to ℍ n +1(−4) × ℝ n and a (k, µ)′ -almost Kenmotsu manifold satisfying any one of the curvature conditions Q(S, R) = 0 or R · R = Q(S, R) is either an Einstein manifold or locally isometric to ℍ n +1(−4) × ℝ n . Finally, an illustrative example is presented.

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.

Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold

2020 ◽  
Vol 70 (1) ◽  
pp. 151-160
Author(s):  
Amalendu Ghosh
Keyword(s):  
Scalar Curvature ◽  
Warped Product ◽  
Constant Scalar Curvature ◽  
Product Structure ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Yamabe Soliton

AbstractIn this paper, we study Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold. First, we prove that if a Kenmotsu metric is a Yamabe soliton, then it has constant scalar curvature. Examples has been provided on a larger class of almost Kenmotsu manifolds, known as β-Kenmotsu manifold. Next, we study quasi Yamabe soliton on a complete Kenmotsu manifold M and proved that it has warped product structure with constant scalar curvature in a region Σ where ∣Df∣ ≠ 0.

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 Certain results on invariant submanifolds of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$-space

2021 ◽  
Author(s):  
Mehmet Atc̣eken
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Curvature ◽  
Invariant Submanifold ◽  
Totally Geodesic ◽  
Ambient Manifold ◽  
Riemannian Curvature Tensor ◽  
Nullity Distribution ◽  
Invariant Submanifolds ◽  
Almost All ◽  
Necessary And Sufficient

AbstractIn the present paper, we study invariant submanifolds of almost Kenmotsu structures whose Riemannian curvature tensor has $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -nullity distribution. Since the geometry of an invariant submanifold inherits almost all properties of the ambient manifold, we research how the functions $$\kappa ,\mu $$ κ , μ and $$\nu $$ ν behave on the submanifold. In this connection, necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -space to be totally geodesic under some conditions.

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