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arXiv · 1201.6455

Biharmonic submanifolds in a Riemannian manifold with non-positive curvature

Nobumitsu Nakauchi·Hajime Urakawa
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Abstract

We show that for an isometric immersion of a complete Riemannian manifold into a Riemannian manifold with non-positive curvature, the norm of the mean curvature vector field is square integrable, then it is minimal. This is a partial affirmative answer of the B. Y. Chen's conjecture.

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Nobumitsu Nakauchi, Hajime Urakawa. 2012-01-31. Biharmonic submanifolds in a Riemannian manifold with non-positive curvature. https://arxiv.org/abs/1201.6455

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