International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 19545, 6 pages

Spacelike hypersurfaces in de Sitter space with constant higher-order mean curvature

Kairen Cai and Huiqun Xu

Department of Mathematics, Hangzhou Teachers College, 222 Wen Yi Road, Hangzhou 310036, China

Received 26 March 2006; Accepted 26 March 2006

Copyright © 2006 Kairen Cai and Huiqun Xu. 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.


The authors apply the generalized Minkowski formula to set up a spherical theorem. It is shown that a compact connected hypersurface with positive constant higher-order mean curvature Hr for some fixed r , 1rn, immersed in the de Sitter space S1n+1 must be a sphere.