Advances in Mathematical Physics
Volume 2012 (2012), Article ID 356263, 18 pages
http://dx.doi.org/10.1155/2012/356263
Research Article

Characterization of Holomorphic Bisectional Curvature of GCR-Lightlike Submanifolds

Sangeet Kumar,1 Rakesh Kumar,2 and R. K. Nagaich3

1Department of Applied Sciences, Rayat Institute of Engineering & Information Technology, Railmajra, SBS Nagar, Punjab 144533, India
2Department of Basic and Applied Sciences, University College of Engineering, Punjabi University, Patiala 147002, India
3Department of Mathematics, Punjabi University, Patiala 147002, India

Received 27 March 2012; Accepted 19 May 2012

Academic Editor: M. Lakshmanan

Copyright © 2012 Sangeet Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite complex space form to be null holomorphically flat. We also obtain some characterization theorems for holomorphic sectional and holomorphic bisectional curvature.