2023/02/19 by Ze-Ping Wang, Wang, Ze-Ping, Ye‐Lin Ou +1
Engineering · Mathematics · #3D Shape Modeling and Analysis #53C12 #53C42 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2302.11545
openalex publication_date 2023/02/19 · openalex created_date 2023/02/24 · openalex updated_date 2026/07/28
In this paper, we study biharmonic Riemannian submersions π:M2×\r→ (N2,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, a proper biharmonic Riemannian submersion π:M2×\r→ (N2,h) is locally a projection of a special twisted product, and when the target surface is non-flat, π 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 H2× \r→ \r2 given by the projection of a warped product.