# Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

Document Type : Research Paper

Authors

1 Department of Mathematics, Punjabi University, Patiala 147 002. India

2 University College of Engineering Punjabi University, Patiala, India

3 Department of Applied Sciences, Chitkara University, India

Abstract

We obtain the expression of Ricci tensor for a $GCR$-lightlike
submanifold of indefinite complex space form and discuss its
properties on a totally geodesic $GCR$-lightlike submanifold of an
indefinite complex space form. Moreover, we have proved that every
proper totally umbilical $GCR$-lightlike submanifold of an
indefinite Kaehler manifold is a totally geodesic $GCR$-lightlike
submanifold.

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### History

• Receive Date: 07 December 2011
• Revise Date: 04 September 2012
• Accept Date: 15 September 2012