Frontiers of Mathematics in China >

2021 , Vol. 16 >Issue 3: 689 - 703

DOI: https://doi.org/10.1007/s11464-021-0938-1

RESEARCH ARTICLE

Characterizations of umbilic hypersurfaces in warped product manifolds

  • Shanze GAO , 1 ,
  • Hui MA 2
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  • 1. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China
  • 2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 10 Nov 2020

Accepted date: 15 Apr 2021

Published date: 15 Jun 2021

Copyright

2021 Higher Education Press
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Abstract

We consider the closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using an 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.

Key words： Umbilic; k-th mean curvature; warped products

Cite this article

Shanze GAO , Hui MA . Characterizations of umbilic hypersurfaces in warped product manifolds[J]. Frontiers of Mathematics in China, 2021 , 16(3) : 689 -703 . DOI: 10.1007/s11464-021-0938-1

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