Spacelike graphs with parallel mean curvature

Details Spacelike graphs with parallel mean curvature Spacelike graphs with parallel mean curvature

2006-02-19

arxiv.org/abs/math/0602410v2

Mathematics

Differential Geometry

11 pages. Some small corrrections of version 1. To appear in the Bull. Belgian Math. Soc. Simon Stevin

Scientific paper

We consider spacelike graphs $\Gamma_f$ of simple products $(M\times N, g\times -h)$ where $(M,g)$ and $(N,h)$ are Riemannian manifolds and $f:M\to N$ is a smooth map. Under the condition of the Cheeger constant of $M$ to be zero and some condition on the second fundamental form at infinity, we conclude that if $\Gamma_f \subset M\times N$ has parallel mean curvature $H$ then $H=0$. This holds trivially if $M$ is closed. If $M$ is the $m$-hyperbolic space then for any constant $c$, we describe a explicit foliation of $H^m\times R$ by hypersurfaces with constant mean curvature $c$.

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