Biharmonic Riemannian submersions

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Akyol M. A., Ou Y.

Annali di Matematica Pura ed Applicata, vol.198, no.2, pp.559-570, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 198 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1007/s10231-018-0789-x
  • Journal Name: Annali di Matematica Pura ed Applicata
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.559-570
  • Keywords: Biharmonic maps, Biharmonic Riemannian submersions, Riemannian submersions, Twisted product, Warped product
  • Uşak University Affiliated: No

Abstract

In this paper, we study biharmonic Riemannian submersions. We first derive bitension field of a general Riemannian submersion, and we then use it to obtain biharmonic equations for Riemannian submersions with one-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 one-dimensional fibers and to characterize warped products whose projections onto the first factor are biharmonic Riemannian submersions.