Minkowski Formulas for compact spacelike hypersurfaces in de Sitter space: Some applications
by
Juan A. Aledo
University of Castilla-La Mancha, Spain
Coauthors: Luis J. Alías (University of Murcia), Alfonso Romero (University of Granada)

Poster

In this paper we develop some integral formulas for compact spacelike hypersurfaces in de Sitter space and apply them in order to characterize the totally umbilical round spheres of de Sitter space as the only compact spacelike hypersurfaces with constant higher order mean curvature, under some appropriate hypothesis. In particular, for hypersurfaces contained in the chronological future (or past) of an equator of de Sitter space we prove that the only compact spacelike hypersurfaces with a constant higher order mean curvature are the totally umbilical round spheres.

Bibliography

- J.A. Aledo, L.J. Alías y A. Romero, Integral formulas for compact space-like hypersurfaces in de Sitter Space. Applications to the case of constant higher order mean curvature. J. Geom. Phys. 31 (1999) 195-208.

Date received: February 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-11.