Harmonic Riemannian submersions from 3-dimensional geometries

2023/02/19 by Zeping Wang, Wang, Ze-Ping, Ye‐Lin Ou +3
Engineering · Physics and Astronomy · #53C43 #58E20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2302.09600

openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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