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

  • Yun, Gab-Jin ;
  • Kim, Dong-Ho
  • Published : 2009.11.30

Abstract

Let M$^n$ be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold N$^{n+p}$ of nonnegative 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;L2 harmonic form

References

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