Harmonic and biharmonic Riemannain submersions from Sol space

2023/02/19 by Wang, Ze-Ping, Ou, Ye-Lin, Liu, Qi-Long · 1 citation
#53C12 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.11693

Abstract

In this paper, we give a complete classification of harmonic and biharmonic Riemannian submersions π:(R³,g_Sol)→ (N²,h) from Sol space into a surface by proving that there is neither harmonic nor biharmonic Riemannian submersion π:(R³,g_Sol)→ (N²,h) from Sol space no matter what the base space (N²,h) is. We also prove that a Riemannian submersion π:(R,g_Sol)→ (N²,h) from Sol space exists only when the base space is a hyperbolic space form.

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• Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature

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