分类： 数学 >> 几何与拓扑 提交时间： 2024-02-28
摘要： In this paper, we study biharmonic Riemannian submersions $ pi:M^2 times r to (N^2,h)$ from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, then a proper biharmonic Riemannian submersion $ pi:M^2 times r to (N^2,h)$ is locally a projection of a special twisted product, and when the target surface is non-flat, $ pi$ is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion $H^2 times r to r^2$ given by the projection of a warped product.
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.
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