L2 Harmonic 1-Forms on Minimal Submanifolds in Spheres

被引：0
|
作者：
Wenzhen Gan
Peng Zhu
机构：
[1] Jiangsu University of Technology,School of Mathematics and Physics
来源：
Results in Mathematics | 2014年 / 65卷
关键词：
53C20; 53C40; harmonic 1-form; total curvature; nonparabolic end;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study a complete noncompact minimal submanifold Mn in a sphere Sn+p. We prove there is no nontrivial L2 harmonic 1-form and at most one nonparabolic end on M if the total curvature is bounded from above by a constant depending only on n. The rigidity theorem is a generalized version of Ni’s, Yun’s and the second author’s results on submanifolds in Euclidean spaces and Seo’s result on minimal submanifolds in hyperbolic spaces.
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页码：483 / 490
页数：7
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