Embedded positive constant r-mean curvature hypersurfaces in Mm × R

Anais da Academia Brasileira de Ciências

Xu Cheng²  Harold Rosenberg¹ 

[1] ,Universidade Federal Fluminense Instituto de Matemática Niterói RJ ,Brasil

关键词: product manifold;    hypersurface;    r-mean curvature;    variedade produto;    hipersuperfície;    curvatura r-média;   

DOI  :  10.1590/S0001-37652005000200001

来源: SciELO

【 摘 要 】

Let M be an m-dimensional Riemannian manifold with sectional curvature bounded from below. We consider hypersurfaces in the (m + 1)-dimensional product manifold M × R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M × R with boundary in M × {0}. We apply this to obtain topological obstructions for the existence of some hypersurfaces. We also discuss the rotational symmetry of some embedded complete surfaces in S² × R of positive constant 2-mean curvature.

【 授权许可】

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