Biharmonic submanifolds in a Riemannian manifold

N. Koiso; H. Urakawa

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arXiv · 1408.5494

Biharmonic submanifolds in a Riemannian manifold

N. Koiso·H. Urakawa

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Abstract

In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal curvatures are simple, and the associated frame field is irreducible.

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N. Koiso, H. Urakawa. 2014-08-23. Biharmonic submanifolds in a Riemannian manifold. https://arxiv.org/abs/1408.5494

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