Non existence of totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds

2015 ◽  
Vol 1 (1041) ◽  
Author(s):  
Varun Jain
Keyword(s):  
Kenmotsu Manifolds ◽  
Lightlike Submanifolds

scholarly journals Geodesic Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
S. M. Khursheed Haider ◽  
Mamta Thakur ◽  
Advin
Keyword(s):  
Kenmotsu Manifolds ◽  
Lightlike Submanifolds

The aim of the present paper is to study geodesic contact screen Cauchy Riemannian (SCR-) lightlike submanifolds, geodesic screen transversal lightlike, and geodesic transversal lightlike submanifolds of indefinite Kenmotsu manifolds.

scholarly journals Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds

2015 ◽  
Vol 46 (2) ◽  
pp. 179-191
Author(s):  
Rashmi Schdeva ◽  
Rakesh Kumar ◽  
Satvinder Singh Bhatia
Keyword(s):  
Space Forms ◽  
Kenmotsu Manifolds ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we study totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds. We prove that there does not exist totally contact umbilical proper slant lightlike submanifold in indefinite Kenmotsu manifolds other than totally contact geodesic proper slant lightlike submanifold. We also prove that there does not exist totally contact umbilical proper slant lightlike submanifold of indefinite Kenmotsu space forms. Finally, we give some characterization theorems on minimal slant lightlike submanifolds of indefinite Kenmotsu manifolds.

scholarly journals Hemi-Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
S. M. Khursheed Haider ◽  
Mamta Thakur ◽  
Advin
Keyword(s):  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We introduce and study hemi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We give an example of hemi-slant lightlike submanifold and establish two characterization theorems for the existence of such submanifolds. We prove some theorems which ensure the existence of minimal hemi-slant lightlike submanifolds and obtain a condition under which the induced connection ∇ on M is a metric connection. An example of proper minimal hemi-slant lightlike submanifolds is also given.

scholarly journals On Parallelism of Half-Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Fundamental Form ◽  
Space Form ◽  
Second Fundamental Form ◽  
Kenmotsu Manifolds ◽  
Lightlike Submanifolds ◽  
Kenmotsu Space Form ◽  
Half Lightlike Submanifold ◽  
Lightlike Submanifold

We mainly investigate the parallelism of half-lightlike submanifolds of indefinite Kenmotsu manifolds. It is proved that a tangential half-lightlike submanifold M of an indefinite Kenmotsu space form M-c,g- with semiparallel second fundamental form h either satisfies c=-1 or is J-RadTM,TM-mixed geodesic.

scholarly journals Screen Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

2010 ◽  
Vol 50 (2) ◽  
pp. 267-279
Author(s):  
Ram Shankar Gupta ◽  
Abhitosh Upadhyay
Keyword(s):  
Kenmotsu Manifolds ◽  
Lightlike Submanifolds

On Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection

2018 ◽  
Vol 48 (1) ◽  
pp. 47-60
Author(s):  
Pradip Majhi ◽  
Ajit Barman ◽  
Uday Chand De
Keyword(s):  
Kenmotsu Manifolds

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 Generalized Transversal Lightlike Submanifolds of Indefinite Sasakian Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Classification Theorem ◽  
Sasakian Manifolds ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We introduce and study generalized transversal lightlike submanifold of indefinite Sasakian manifolds which includes radical and transversal lightlike submanifolds of indefinite Sasakian manifolds as its trivial subcases. A characteristic theorem and a classification theorem of generalized transversal lightlike submanifolds are obtained.

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