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

Nagaich, R.; Kumar, R.; Kumar, S.

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.

Keywords

Main Subjects