Biharmonic Riemannian submersions

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.

14 pages

References in corpus (1)

• Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps

Cited by in corpus (2)

• Biconservative quasi-minimal immersions into semi-Euclidean spaces
• Harmonic maps and biharmonic Riemanian submersions