THE MÖBIUS CHARACTERIZATIONS OF WILLMORE TORI AND VERONESE SUBMANIFOLDS IN THE UNIT SPHERE
THE MÖBIUS CHARACTERIZATIONS OF WILLMORE TORI AND VERONESE SUBMANIFOLDS IN THE UNIT SPHERE
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DOI：
10.2140/pjm.2009.241.227
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发表时间：
2009-06
影响因子：
0.6
通讯作者：
Zhen Guo;Haizhong Li;Changping Wang
中科院分区：
文献类型：
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作者：
Zhen Guo;Haizhong Li;Changping Wang
设M是(m+p)维单位球面Sm+p中无脐点的m维子流形.在Sm+p的Mobius变换群下，Mm的四个基本不变量是一个称为Mobius度规的对称正定2-形式g，一个称为Mobius第二基本形式的法丛B截面，一个称为Mobius形式的1-形式F，以及一个称为Blaschke张量的对称(0，2)张量A.在子流形的Mobius几何中，Mobius极小子流形(又称Willmore子流形)的最重要的例子是Willmore Tori和Verones子流形。本文建立了子流形的Mobius几何的几个基本不等式，并利用Mobius不变量给出了Willmore Tori和Verones子流形的Mobius刻画。
Suppose M is a m-dimensional submanifold without umbilic points in the (m + p)-dimensional unit sphere Sm+p. Four basic invariants of Mm under the Mobius transformation group of Sm+p are a symmetric positive definite 2-form g called the Mobius metric, a section B of the normal bundle called the Mobius second fundamental form, a 1-form F called the Mobius form, and a symmetric (0,2) tensor A called the Blaschke tensor. In the Mobius geometry of submanifolds, the most important examples of Mobius minimal submanifolds (also called Willmore submanifolds) are Willmore tori and Veronese submanifolds. In this paper, several fundamental inequalities of the Mobius geometry of submanifolds are established and the Mobius characterizations of Willmore tori and Veronese submanifolds are presented by using Mobius invariants.