Pseudo-umbilical spacelike submanifolds of de-Sitter space

Pseudo-umbilical spacelike submanifolds of de-Sitter space

In 1970 Chern, do Carmo and Kobayashi [2] generalized the result of Lawson [5] from minimal hypersurfaces to submanifolds of a sphere. Later analogously T. Ishihara [4] investigated maximal spacelike submanifolds of pseudo-Riemannian space of constant curvature (or de-Sitter space). On the other hand Deshmukh [3] studied minimal submanifolds of a sphere and concluded some interesting results and showed that minimal submanifolds of a sphere are totally geodesic under certain geometric conditions. In this paper we generalize the results of [3] to pseudo-umbilical spacelike submanifolds of de-Sitter space.

In 1970 Chern, do Carmo and Kobayashi [2] generalized the result of Lawson [5] from minimal hypersurfaces to submanifolds of a sphere. Later analogously T. Ishihara [4] investigated maximal spacelike submanifolds of pseudo-Riemannian space of constant curvature (or de-Sitter space). On the other hand Deshmukh [3] studied minimal submanifolds of a sphere and concluded some interesting results and showed that minimal submanifolds of a sphere are totally geodesic under certain geometric conditions. In this paper we generalize the results of [3] to pseudo-umbilical spacelike submanifolds of de-Sitter space.