scholarly journals Harmonic Maps and Stability onf-Kenmotsu Manifolds

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Vittorio Mangione
Keyword(s):  
Harmonic Maps ◽  
Riemannian Submersions ◽  
Kenmotsu Manifold ◽  
Holomorphic Map ◽  
Kenmotsu Manifolds ◽  
The Stability ◽  
Kählerian Manifold

The purpose of this paper is to study some submanifolds and Riemannian submersions on anf-Kenmotsu manifold. The stability of aϕ-holomorphic map from a compactf-Kenmotsu manifold to a Kählerian manifold is proven.

scholarly journals Harmonic Maps on Kenmotsu Manifolds

2013 ◽  
Vol 21 (3) ◽  
pp. 197-208
Author(s):  
Najma Abdul Rehman
Keyword(s):  
Spectral Theory ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Harmonic Morphisms ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Target Manifold

AbstractWe study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.

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.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

scholarly journals Some Results on Weakly Symmetric Kenmotsu Manifolds

2019 ◽  
Vol 7 (1) ◽  
pp. 13-21
Author(s):  
J. P. Singh ◽  
◽  
K. Lalnunsiami
Keyword(s):  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Weakly Symmetric ◽  
Symmetric Properties

In this paper, we investigate weakly symmetric, weakly Ricci symmetric, weakly concircular symmetric and weakly concircular Ricci symmetric properties of a Kenmotsu manifold admitting a semi-symmetric metric connection. Some results on weakly -projectively symmetric Kenmotsu manifold with respect to a semi-symmetric metric connection are obtained. An example of a weakly symmetric and weakly Ricci symmetric Kenmotsu manifold with respect to this connection is constructed.

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 Kenmotsu manifolds admitting Schouten-Van Kampen Connection

2019 ◽  
pp. 23
Author(s):  
Nagaraja Gangadharappa Halammanavar ◽  
Kiran Kumar Lakshmana Devasandra
Keyword(s):  
Ricci Soliton ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Equivalent Conditions

The objective of the present paper is to study Kenmotsu manifold admitting Schouten-van Kampen connection. We study Kenmotsu manifold admitting Schouten-van Kampen connection satisifying certain curvature conditions. Also we prove equivalent conditions for Ricci soliton in a Kenmotsu manifold is steady with respect to the Schouten-van Kampen connection.

scholarly journals Some Symmetric Properties of Kenmotsu Manifolds Admitting Semi-Symmetric Metric Connection

2019 ◽  
pp. 35
Author(s):  
Venkatesha Venkatesh ◽  
Arasaiah Arasaiah ◽  
Vishnuvardhana Srivaishnava Vasudeva ◽  
Naveen Kumar Rahuthanahalli Thimmegowda
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Symmetric Properties

The object of the present paper is to study some symmetric propertiesof Kenmotsu manifold endowed with a semi-symmetric metric connection. Here weconsider pseudo-symmetric, Ricci pseudo-symmetric, projective pseudo-symmetric and -projective semi-symmetric Kenmotsu manifold with respect to semi-symmetric metric connection. Finally, we provide an example of 3-dimensional Kenmotsu manifold admitting a semi-symmetric metric connection which verify our results.

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.

Stability and constant boundary-value problems of harmonic maps with potential

2000 ◽  
Vol 68 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Qun Chen
Keyword(s):  
Riemannian Manifold ◽  
Energy Density ◽  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
General Class ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Boundary Value ◽  
The Stability ◽  
Harmonic Maps With Potential

AbstractLet M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.

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