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Vietnam Journal of Mathematics 39:1 (2011) 91-103 

Totally Contact Umbilical GCR-Lightlike

Submanifolds Indefinite Sasakian Manifolds

Varun Jain, Rakesh Kumar and Rakesh Kumar Nagaich

 

Abstract. In the present paper we find the conditions for the integrability of the distributions $\var D$ and D{V} of a GCR-lightlike submanifold M of an indefinite Sasakian manifold $\var M$. We find the conditions for the distributions $\var D$ and D {V} to define totally geodesic foliation in M and for the characterization of the connection to be a metric connection on the lightlike submanifold M. Finally, we study totally contact umbilical GCR-lightlike submanifolds and prove that a totally contact umbilical GCR-lightlike submanifold is a totally contact geodesic and a totally geodesic GCR-lightlike submanifold.

2000 Mathematics Subject Classification: 53C15, 53C40, 53C50.

Keywords: Indefinite Sasakian Manifolds, GCR-Lightlike Submanifolds, Totally Contact Umbilical GCR-Lightlike Submanifolds.

 

 

 

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