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arXiv · 2302.09600

Harmonic Riemannian submersions from 3-dimensional geometries

Ze-Ping Wang·Ye-Lin Ou·Yong-Gui Luo
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Abstract

In this paper, we study harmonic Riemannian submersions from 3-dimensional geometries using the ( generalized) integrability data associated to an orthonormal frame natural to a Riemannian submersion. We give complete classifications of harmonic Riemannian submersions from Thurston's 3-dimensional geometries, 3-dimensional BCV spaces and Berger sphere into a surface. We also give some explicit constructions of these harmonic Riemannian submersions.

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Ze-Ping Wang, Ye-Lin Ou, Yong-Gui Luo. 2023-02-19. Harmonic Riemannian submersions from 3-dimensional geometries. https://arxiv.org/abs/2302.09600

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