Characterizations of umbilic hypersurfaces in warped product manifolds |
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Authors: | Shanze GAO Hui MA |
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Institution: | 1. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China2. 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. |
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Keywords: | Umbilic k-th mean curvature warped products |
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