Table of Contents
ISRN Geometry
Volume 2014 (2014), Article ID 974695, 10 pages
http://dx.doi.org/10.1155/2014/974695
Research Article

Totally Umbilical Lightlike Hypersurfaces in Robertson-Walker Spacetimes

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 25 January 2014; Accepted 24 February 2014; Published 18 March 2014

Academic Editors: T. Friedrich and S. Hervik

Copyright © 2014 Junhong Dong and Ximin Liu. 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 study the problem of lightlike hypersurface immersed into Robertson-Walker (RW) spacetimes in this paper, where the screen bundle of the hypersurface has constant higher order mean curvature. We consider the following question: under what conditions is the compact lightlike hypersurface totally umbilical? Our approach is based on the relationship between the lightlike hypersurface with its screen bundle and the Minkowski formulae for the screen bundle.