Table of Contents
Geometry
Volume 2013, Article ID 549602, 9 pages
http://dx.doi.org/10.1155/2013/549602
Research Article

Conformal Geometry of Hypersurfaces in Lorentz Space Forms

1Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
2Faculty of Mathematics and Computer Sciences, Hubei University, Wuhan 430062, China

Received 22 June 2013; Accepted 8 August 2013

Academic Editor: Anna Fino

Copyright © 2013 Tongzhu Li and Changxiong Nie. 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

Let be a space-like hypersurface without umbilical points in the Lorentz space form . We define the conformal metric and the conformal second fundamental form on the hypersurface, which determines the hypersurface up to conformal transformation of . We calculate the Euler-Lagrange equations of the volume functional of the hypersurface with respect to the conformal metric, whose critical point is called a Willmore hypersurface, and we give a conformal characteristic of the hypersurfaces with constant mean curvature and constant scalar curvature. Finally, we prove that if the hypersurface with constant mean curvature and constant scalar curvature is Willmore, then is a hypersurface in .