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Biharmonic isometric immersions into and biharmonic Riemannian submersions from Berger 3-spheres

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摘要: In this paper, we study biharmonic isometric immersions of a surface into and biharmonic Riemannian submersions from 3-dimensional Berger spheres. We obtain a classifification of proper biharmonic isometric immersions of a surface with constant mean curvature into Berger 3-spheres. We also give a complete classifification of proper biharmonic Hopf tori in Berger 3-sphere.
For Riemannian submersions, we prove that a Riemannian submersion from Berger 3-spheres into a surface is biharmonic if and only if it is harmonic.

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[V1] 2023-02-22 16:23:45 ChinaXiv:202302.00247V1 下载全文
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