Characterizations of umbilic hypersurfaces in warped product manifolds

doi:10.1007/s11464-021-0938-1

Front. Math. China

2021, Vol. 16

Issue (3) : 689-703 https://doi.org/10.1007/s11464-021-0938-1

RESEARCH ARTICLE

Characterizations of umbilic hypersurfaces in warped product manifolds

Shanze GAO¹(

), Hui MA²

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

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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.

Keywords Umbilic k-th mean curvature warped products

Corresponding Author(s): Shanze GAO

Issue Date: 14 July 2021

Cite this article:

Shanze GAO,Hui MA. Characterizations of umbilic hypersurfaces in warped product manifolds[J]. Front. Math. China, 2021, 16(3): 689-703.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0938-1
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I3/689

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