分类: 数学 >> 几何与拓扑 提交时间: 2023-02-22
摘要: In this paper, we give a complete classifification of harmonic and biharmon#2; ic Riemannian submersions : (R^3 , g_Sol) (N^2 , h) from Sol space into a surface by proving that there is neither harmonic nor biharmonic Riemann#2; ian submersion : (R^3 , g_Sol) (N^2 , h) from Sol space no matter what the base space (N2 , h) is. We also prove that a Riemannian submersion : (R^3 , g_Sol) (N^2 , h) from Sol space exists only when the base space is a hyperbolic space form.
分类: 数学 >> 几何与拓扑 提交时间: 2023-02-22
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.