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arXiv · 2109.12687

Bi-eigenmaps and biharmonic submanifolds in a sphere

Ye-Lin Ou
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Abstract

In this note, we classify biharmonic submanifolds in a sphere defined by bi-eigenmaps ($\Delta^2 \phi=\lambda \phi$) or buckling eigenmaps ($\Delta^2 \phi=-\mu \Delta \phi$). We then classify biharmonic bi-eigenmaps and buckling eigenmaps into spheres with constant energy density. The results can be viewed as generalizations of Takahashi's characterization of minimal submanifolds in a sphere by eigenmaps.

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Ye-Lin Ou. 2021-09-26. Bi-eigenmaps and biharmonic submanifolds in a sphere. https://arxiv.org/abs/2109.12687

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