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Characterizations of umbilic hypersurfaces in warped product manifolds

Shanze Gao University of Science and Technology of China Hui Ma Tsinghua University

Differential Geometry mathscidoc:1908.10013

2019.2
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. In particular, Corollary 1.8 implies that the embeddedness condition in Theorem 2 of [Brendle-Eichmair, JDG. 2013] is not necessary.
umbilic, $k$-th mean curvature, warped products
[ Download ] [ 2019-08-28 11:01:22 uploaded by Laxpair ] [ 617 downloads ] [ 0 comments ]
  • Submitted.
@inproceedings{shanze2019characterizations,
  title={Characterizations of umbilic hypersurfaces in warped product manifolds},
  author={Shanze Gao, and Hui Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190828110122404705468},
  year={2019},
}
Shanze Gao, and Hui Ma. Characterizations of umbilic hypersurfaces in warped product manifolds. 2019. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190828110122404705468.
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