Spacelike graphs with parallel mean curvature

2006/02/19 by Isabel M. C. Salavessa, Salavessa, Isabel M. C. · 1 citation
Mathematics · Physics and Astronomy · #53C42 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C42 #msc:53C50

paper · pdf · doi:10.48550/arxiv.math/0602410

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

openalex publication_date 2006/02/19 · arxiv created 2007/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider spacelike graphs Γ_f of simple products (M× N, g× -h) where (M,g) and (N,h) are Riemannian manifolds and f:M→ 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 Γ_f ⊂ M× 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× R by hypersurfaces with constant mean curvature c.

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