Conformal Invariants of Submanifolds in a Riemannian Space and Conformal Rigidity Theorems on Willmore Hypersurfaces

被引：3

作者：

Guo, Zhen ^{[1
]}

Li, Hong ^{[1
]}

机构：

[1] Yunnan Normal Univ, Dept Math, Kunming, Yunnan, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2018年 / 28卷 / 03期

关键词：

Submanifolds; Conformal invariant; Integral inequality; Willmore tori; MOBIUS ISOPARAMETRIC HYPERSURFACES; DISTINCT PRINCIPAL CURVATURES; MEAN-CURVATURE; CLASSIFICATION; GEOMETRY; FORM;

D O I：

10.1007/s12220-017-9928-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The conformal geometry of submanifolds in a constant curvature space was well studied in the past 15 years. The first part of this paper presents the system of complete conformal invariants of submanifolds in a general Riemannian space, and the second part presents several conformal rigidity theorems on compact Willmore hypersurfaces. In particular, the conformal class of Willmore tori is characterized using a conformal invariant.

引用

页码：2670 / 2691

页数：22

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