CMC hypersurfaces on riemannian and semi-riemannian manifolds

2009/04/13 by Oscar Perdomo, Perdomo, Oscar
Mathematics · Physics and Astronomy · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C42

paper · pdf · doi:10.48550/arxiv.0904.1984

20 pages

arxiv created 2009/04/13 · arxiv updated 2009/12/01

Abstract

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 sqrtn-1/n) can be realized as the constant curvature of a complete immersion of S₁^n-1 x R in the (n+1)-dimensional de Sitter space S₁ⁿ⁺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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