Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (6): 1609-1618.doi: 10.1016/S0252-9602(16)30093-5

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RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE

Jing WANG1, Yinshan ZHANG2   

  1. 1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2015-07-25 Revised:2016-03-28 Online:2016-12-25 Published:2016-12-25
  • Contact: Yinshan ZHANG,E-mail:zhangysookk@163.com E-mail:zhangysookk@163.com
  • Supported by:

    This work was supported by NSFC (11371330).

Abstract:

In this paper, we establish a rigidity theorem for compact constant mean curvature surfaces of the Berger sphere in terms of the surfaces' geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.

Key words: homogeneous 3-manifolds, Berger sphere, constant mean curvature surface, Hopf torus, Clifford torus

CLC Number: 

  • 53C24
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