Article ID Journal Published Year Pages File Type
4615828 Journal of Mathematical Analysis and Applications 2014 7 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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