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arXiv · 2002.04196

Stability and the index of biharmonic hypersurfaces in a Riemannian manifold

Ye-Lin Ou
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Abstract

In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riamannian manifold similar to that of a minimal hypersurface. We then use the second variation formula to compute the stability index of the known biharmonic hypersurfaces in a Euclidean sphere, and to prove the non-existence of unstable proper biharmonic hypersurface in a Euclidean space or a hyperbolic space, which adds another special case to support Chen's conjecture on biharmonic submanifolds.

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Ye-Lin Ou. 2020-02-11. Stability and the index of biharmonic hypersurfaces in a Riemannian manifold. https://arxiv.org/abs/2002.04196

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