A gap theorem on submanifolds with finite total curvature in spheres
A gap theorem on submanifolds with finite total curvature in spheres
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DOI：
10.1016/j.jmaa.2013.11.064
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发表时间：
2014-05
影响因子：
1.3
通讯作者：
P. Zhu;Shouwen Fang
中科院分区：
文献类型：
--
作者：
P. Zhu;Shouwen Fang
研究了球面S n+p中的完备非紧子流形M_n，证明了如果M上的总曲率由一个仅依赖于n的常数从上有界，则M上不允许有非平凡的L 2-调和1-形式.间隙定理是CarronʼS，YunʼS，CavalcanteʼS和第一作者ʼS关于欧氏空间中的子流形的结果和SeoʼS关于双曲空间中的子流形的结果的推广.
We study a complete noncompact submanifold M n in a sphere S n+ p. We prove that there admit no nontrivial L 2-harmonic 1-forms on M if the total curvature is bounded from above by a constant depending only on n. The gap theorem is a generalized version of Carronʼs, Yunʼs, Cavalcanteʼs and the first authorʼs results on submanifolds in Euclidean spaces and Seoʼs result on submanifolds in hyperbolic space without the condition of minimality.