CMC hypersurfaces on riemannian and semi-riemannian manifolds

Details CMC hypersurfaces on riemannian and semi-riemannian manifolds CMC hypersurfaces on riemannian and semi-riemannian manifolds

2009-04-13

arxiv.org/abs/0904.1984v1

Mathematics

Differential Geometry

20 pages

Scientific paper

In this paper we show explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-riemannian manifolds with constant sectional curvature. In particular, we prove that every h in [-1,-2 sqrt{n-1}/n) can be realized as the constant curvature of a complete immersion of S_1^{n-1} x R in the (n+1)-dimensional de Sitter space S_1^{n+1}. We provide 3 types of immersions with cmc in the Minkowski space, 5 types of immersion with cmc in the de Sitter space and 5 types of immersion with cmc in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.

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