On the structure of minimal submanifolds in a Riemannian manifold of non-negative curvature
Bull. Korean Math. Soc. 2009 Vol. 46, No. 6, 1213-1219
Published online November 1, 2009
Gabjin Yun and Dongho Kim
Myong Ji University and Myong Ji University
Abstract : Let $M^{n}$ be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold $N^{n+p}$ of non-negative curvature. We prove that if $M$ is super-stable, then there are no non-trivial $L^2$ harmonic one forms on $M$. This is a generalization of the main result in [8].
Keywords : minimal submanifold, super-stable minimal submanifold, $L^2$ harmonic form
MSC numbers : 53C21
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