Biharmonic Riemannian submersions

2018/05/12 by Mehmet Akif Akyol, Akyol, Mehmet Akif, Ye‐Lin Ou +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1805.04745

openalex publication_date 2018/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature

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