On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian

Hakan Mete Taṣtan, Fatma Özdemir, Cem Sayar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.

Original languageEnglish
Pages (from-to)411-422
Number of pages12
JournalJournal of Geometry
Volume108
Issue number2
DOIs
Publication statusPublished - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Keywords

  • anti-invariant submersions
  • first variational formula
  • horizontal distribution
  • Lagrangian submersion
  • locally product Riemannian manifold
  • Riemannian submersion

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