Characterizations of umbilic hypersurfaces in warped product manifolds

Shanze GAO; Hui MA

doi:10.1007/s11464-021-0938-1

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Front. Math. China ›› 2021, Vol. 16 ›› Issue (3) : 689-703. DOI: 10.1007/s11464-021-0938-1

RESEARCH ARTICLE

Characterizations of umbilic hypersurfaces in warped product manifolds

Shanze GAO¹ ,
Hui MA²

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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

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Shanze GAO, Hui MA. Characterizations of umbilic hypersurfaces in warped product manifolds. Front. Math. China, 2021, 16(3): 689‒703 https://doi.org/10.1007/s11464-021-0938-1

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