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February 2008 Spacelike Graphs with Parallel Mean Curvature
Isabel M.C. Salavessa
Bull. Belg. Math. Soc. Simon Stevin 15(1): 65-76 (February 2008). DOI: 10.36045/bbms/1203692447


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 $f:M\rightarrow N$ 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 an explicit foliation of $ {\mathbb H}^m\times \mathbb R$ by hypersurfaces with constant mean curvature $c$.


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Isabel M.C. Salavessa. "Spacelike Graphs with Parallel Mean Curvature." Bull. Belg. Math. Soc. Simon Stevin 15 (1) 65 - 76, February 2008.


Published: February 2008
First available in Project Euclid: 22 February 2008

zbMATH: 1146.53036
MathSciNet: MR2406087
Digital Object Identifier: 10.36045/bbms/1203692447

Primary: 53C42 , 53C50

Keywords: Isoperimetric inequality , Lorentzian manifold , Parallel and Constant Mean curvature , space-like hypersurface

Rights: Copyright © 2008 The Belgian Mathematical Society


Vol.15 • No. 1 • February 2008
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