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

Tastan H. M., Özdemir F., Sayar C.

JOURNAL OF GEOMETRY, vol.108, no.2, pp.411-422, 2017 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 108 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s00022-016-0347-x
  • Journal Name: JOURNAL OF GEOMETRY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.411-422
  • Istanbul University Affiliated: Yes

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.