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2009•Bulletin of the Korean Mathematical SocietyOpen access

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

Gabjin Yun, Dongho Kim

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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].

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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].

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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].

Key concepts: Mathematics, Submanifold, Riemannian manifold, Pure mathematics, Generalization, Ricci curvature, Curvature, Manifold (fluid mechanics)

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