Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(4): 1173-1192

Printed July 1, 2013

https://doi.org/10.4134/BKMS.2013.50.4.1173

Copyright © The Korean Mathematical Society.

$GCR$-lightlike submanifolds of indefinite nearly Kaehler manifolds

Sangeet Kumar, Rakesh Kumar, and R. K. Nagaich

Chitkara University, Punjabi University, Punjabi University

Abstract

We introduce $CR$, $SCR$ and $GCR$-lightlike submanifolds of indefinite nearly Kaehler manifolds and obtain their existence in indefinite nearly Kaehler manifolds of constant holomorphic sectional curvature $c$ and of constant type $\alpha$. We also prove characterization theorems on the existence of totally umbilical and minimal $GCR$-lightlike submanifolds of indefinite nearly Kaehler manifolds.

Keywords: indefinite nearly Kaehler manifolds, $CR$-lightlike submanifolds, $SCR$-lightlike submanifolds, $GCR$-lightlike submanifolds, totally umbilical lightlike submanifolds, minimal lightlike submanifolds

MSC numbers: 53C15, 53C40, 53C50

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