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arXiv · 1805.04745

Biharmonic Riemannian submersions

Mehmet Akif Akyol·Ye-Lin Ou
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Abstract

In this paper, we study biharmonic Riemannian submersions. We first derive bitension field of a general Riemannian submersion, we then use it to obtain biharmonic equations for Riemannian submersions with $1$-dimensional fibers and Riemannian submersions with basic mean curvature vector fields of fibers. These are used to construct examples of proper biharmonic Riemannian submersions with $1$-dimensional fibers and to characterize warped products whose projections onto the first factor are biharmonic Riemannian submersions.

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Mehmet Akif Akyol, Ye-Lin Ou. 2018-05-12. Biharmonic Riemannian submersions. https://arxiv.org/abs/1805.04745

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