Bull. Korean Math. Soc. 2009; 46(6): 1213-1219
Printed November 1, 2009
https://doi.org/10.4134/BKMS.2009.46.6.1213
Copyright © The Korean Mathematical Society.
Gabjin Yun and Dongho Kim
Myong Ji University and Myong Ji University
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
2013; 50(4): 1201-1207
2013; 50(1): 135-142
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