The Mbius characterizations of Willmore tori and Veronese submanifolds in the unit sphere

Feng Luo Haizhong Li Changping Wang

Differential Geometry mathscidoc:1912.43786

Pacific journal of mathematics, 241, (2), 227-242, 2009.6
Suppose M is a m-dimensional submanifold without umbilic points in the (m+ p)-dimensional unit sphere S m+ p. Four basic invariants of M m under the Mbius transformation group of S m+ p are a symmetric positive definite 2-form g called the Mbius metric, a section B of the normal bundle called the Mbius second fundamental form, a 1-form called the Mbius form, and a symmetric (0, 2) tensor A called the Blaschke tensor. In the Mbius geometry of submanifolds, the most important examples of Mbius minimal submanifolds (also called Willmore submanifolds) are Willmore tori and Veronese submanifolds. In this paper, several fundamental inequalities of the Mbius geometry of submanifolds are established and the Mbius characterizations of Willmore tori and Veronese submanifolds are presented by using Mbius invariants.
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@inproceedings{feng2009the,
  title={The Mbius characterizations of Willmore tori and Veronese submanifolds in the unit sphere},
  author={Feng Luo, Haizhong Li, and Changping Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205816477236350},
  booktitle={Pacific journal of mathematics},
  volume={241},
  number={2},
  pages={227-242},
  year={2009},
}
Feng Luo, Haizhong Li, and Changping Wang. The Mbius characterizations of Willmore tori and Veronese submanifolds in the unit sphere. 2009. Vol. 241. In Pacific journal of mathematics. pp.227-242. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205816477236350.
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