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Rigidity theorems of hypersurfaces in locally symmetric Riemannian manifold


Authors: Shicheng Zhang and Baoqiang Wu
Journal: Proc. Amer. Math. Soc. 141 (2013), 4015-4025
MSC (2010): Primary 53B20, 53C24, 53C20
DOI: https://doi.org/10.1090/S0002-9939-2013-11780-6
Published electronically: July 12, 2013
MathSciNet review: 3091792
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Abstract: In this paper, the linear Weingarten hypersurfaces in a locally symmetric Riemannian manifold are investigated and the rigidity theorems are proved by the operator $ \Box $ introduced by S. Y. Cheng and S. T. Yau, which is a generalization of main results obtained by several authors.


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Additional Information

Shicheng Zhang
Affiliation: School of Mathematics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China
Email: zhangshicheng@jsnu.edu.cn

Baoqiang Wu
Affiliation: School of Mathematics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China
Email: wubaoqiang@jsnu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11780-6
Keywords: Locally symmetric, linear Weingarten hypersurfaces, totally umbilical
Received by editor(s): January 10, 2012
Published electronically: July 12, 2013
Additional Notes: This work was supported by the National Natural Science Foundation of China (No. 10871218, No. 61271002 and No. 10932002) and the Natural Science Foundation of Xuzhou Normal University (No. 11XLR36).
Communicated by: Lei Ni
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.