Abstract

BARREIRO CHAVES, Rosa Maria S.  and  SOUSA, Luiz Amancio M.. On Complete Spacelike Submanifolds in the De Sitter Space With Parallel Mean Curvature Vector. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.1, pp.85-98. ISSN 0041-6932.

The text surveys some results concerning submanifolds with parallel mean curvature vector immersed in the De Sitter space. We also propose a semi-Riemannian version of an important inequality obtained by Simons in the Riemannian case and apply it in order to obtain some results characterizing umbilical submanifolds and a product of submanifolds in the (n + p)-dimensional De Sitter space .

Keywords : De Sitter space; Simons type formula; complete spacelike submanifolds; parallel mean curvature vector.

        · text in English     · English ( pdf )