On rigidity phenomena of compact surfaces in homogeneous $3$-manifolds
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- by Zejun Hu, Dongliang Lyu and Jing Wang PDF
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Abstract:
Let $E(\kappa ,\tau )$ be the $3$-dimensional homogeneous Riemannian manifold with isometry group of dimension $4$, where $\kappa$ is the curvature of the basis and $\tau$ the bundle curvature, which satisfy $\kappa -4\tau ^2\not =0$. A special case of $E(\kappa ,\tau )$ is the Berger sphere that is also denoted by $\mathbb {S}^3_b(\kappa ,\tau )$. In this paper, surfaces of $E(\kappa ,\tau )$ are studied. As the main result, rigidity theorems in terms of the second fundamental form are established for compact (minimal) surfaces of $\mathbb {S}^3_b(\kappa ,\tau )$.References
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Additional Information
- Zejun Hu
- Affiliation: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, People’s Republic of China
- MR Author ID: 346519
- ORCID: 0000-0003-2744-5803
- Email: huzj@zzu.edu.cn
- Dongliang Lyu
- Affiliation: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, People’s Republic of China
- Email: dongliang040@sina.com
- Jing Wang
- Affiliation: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, People’s Republic of China
- Address at time of publication: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102400, People’s Republic of China
- Email: wangjingzzumath@163.com
- Received by editor(s): April 21, 2013
- Received by editor(s) in revised form: August 3, 2013, and August 17, 2013
- Published electronically: March 18, 2015
- Additional Notes: This project was supported by grants of NSFC-11071225 and NSFC-11371330.
- Communicated by: Lei Ni
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 3097-3109
- MSC (2010): Primary 53C24; Secondary 53C20, 53C42
- DOI: https://doi.org/10.1090/S0002-9939-2015-12356-8
- MathSciNet review: 3336634