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Biharmonic Riemannian submersions from the product space $M^2 times r$

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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.

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[V2] 2024-02-28 13:08:55 ChinaXiv:202302.00251V2 下载全文
[V1] 2023-02-22 15:47:04 ChinaXiv:202302.00251v1 查看此版本 下载全文
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