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arXiv · 2611.04159

Biharmonic submanifolds in nonpositive space forms

Yu Fu·Min-chun Hong·Dan Yang
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Abstract

We prove that there are no proper biharmonic submanifolds with parallel normalized mean curvature vector field in a nonpositive space form, in arbitrary dimension and codimension. We also prove that every biharmonic surface with flat normal bundle in a four-dimensional nonpositive space form is minimal. These results provide substantial support for Chen's conjecture and the generalized Chen's conjecture for hyperbolic space in higher codimensions.

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Yu Fu, Min-chun Hong, Dan Yang. 2026-11-03. Biharmonic submanifolds in nonpositive space forms. https://arxiv.org/abs/2611.04159

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