@article{
author = {Wang, Zeping; Ou, Yelin; },
title = {Biharmonic Riemannian submersions from the product space $M^2 times r$},
keywords = {Biharmonic maps; biharmonic Riemannian submersions; product spaces},
abstract = {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.},
doi = {10.12074/202302.00251V1},
url = {https://chinaxiv.org/abs/202302.00251},
timestamp = {2024-05-25},
}