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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On rigidity phenomena of compact surfaces in homogeneous $3$-manifolds
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by Zejun Hu, Dongliang Lyu and Jing Wang PDF
Proc. Amer. Math. Soc. 143 (2015), 3097-3109 Request permission

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