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arXiv · 1902.04799

Characterizations of umbilic hypersurfaces in warped product manifolds

Shanze Gao·Hui Ma
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Abstract

We consider closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordstr\"{o}m manifolds. By using a new integral formula or Brendle's Heintze-Karcher type inequality, we present some new characterizations of umbilic hypersurfaces. These results can be viewed as generalizations of the classical Jellet-Liebmann theorem and the Alexandrov theorem in Euclidean space.

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Shanze Gao, Hui Ma. 2019-02-13. Characterizations of umbilic hypersurfaces in warped product manifolds. https://arxiv.org/abs/1902.04799

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