Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615828 | Journal of Mathematical Analysis and Applications | 2014 | 7 Pages |
Abstract
We study a complete noncompact submanifold MnMn in a sphere Sn+pSn+p. We prove that there admit no nontrivial L2L2-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.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Peng Zhu, Shouwen Fang,