ON THE STRUCTURE OF MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF NON-NEGATIVE CURVATURE

Title & Authors
ON THE STRUCTURE OF MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF NON-NEGATIVE CURVATURE
Yun, Gab-Jin; Kim, Dong-Ho;

Abstract
Let M$\small{^n}$ be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold N$\small{^{n+p}}$ of nonnegative curvature. We prove that if M is super-stable, then there are no non-trivial L$\small{^2}$ harmonic one forms on M. This is a generalization of the main result in [8].
Keywords
minimal submanifold;super-stable minimal submanifold;L2 harmonic form;
Language
English
Cited by
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