Complete spacelike hypersurfaces with constant mean curvature in the de Sitter space: a gap theorem. (English) Zbl 1047.53031

Brasil, Aldir jun.; Colares, A. Gervasio; Palmas, Oscar

Ill. J. Math. 47, No. 3, 847-866 (2003).

The authors study the topology and geometry of space-like surfaces with constant mean curvature in de Sitter space. Their result is a Lorentzian analogue of a theorem of H. Alencar and M. P. do Carmo [Proc. Am. Math. Soc. 120, 1223–1229 (1994; Zbl 0802.53017)] about hypersurfaces in the sphere. They give a lot of explicit examples of such hypersurfaces.

Reviewer: Jean-François Quint (Villeurbanne)

MSC:

53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

de Sitter space; subvariety; curvature

Citations:

Zbl 0802.53017