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Recent
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Volume 52
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Volume 51
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Volume 50
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Volume 49
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Volume
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Vietnam
Journal of Mathematics 39:1 (2011) 91-103
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Totally Contact Umbilical GCR-Lightlike
Submanifolds Indefinite Sasakian Manifolds
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Varun Jain, Rakesh
Kumar and Rakesh Kumar Nagaich
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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.
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2000 Mathematics Subject Classification: 53C15, 53C40,
53C50.
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Keywords: Indefinite Sasakian Manifolds,
GCR-Lightlike Submanifolds, Totally Contact
Umbilical GCR-Lightlike Submanifolds.
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Vietnam Academy of Science and Technology &
Vietnamese Mathematical Society
©
Copyright Vietnam
Journal of Mathematics. All rights reserved.
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