CLAIRAUT ANTI-INVARIANT SUBMERSIONS FROM COSYMPLECTIC MANIFOLDS

Tastan H. M., Gerdan Aydın S.

HONAM MATHEMATICAL JOURNAL, vol.41, no.4, pp.707-724, 2019 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.5831/hmj.2019.41.4.707
  • Journal Name: HONAM MATHEMATICAL JOURNAL
  • Page Numbers: pp.707-724
  • Keywords: Riemannian submersion, anti-invariant submersion, Lagrangian submersion, Clairaut submersion, cosymplectic manifold, RIEMANNIAN SUBMERSIONS
  • Istanbul University Affiliated: Yes

Abstract

We investigate the new Clairaut conditions for antiinvariant submersions whose total manifolds are cosymplectic. In particular, we prove the fibers of a proper Clairaut Lagrangian submersion admitting horizontal Reeb vector field are one dimensional and classify such submersions. We also check the existence of the proper Clairaut anti-invariant submersions in the case of the Reeb vector field is vertical. Moreover, illustrative examples for both trivial and proper Clairaut anti-invariant submersions are given.