Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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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.

On the structure of minimal submanifolds in a Riemannian manifold of non-negative curvature

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