Certain curves along Riemannian submersions

ÖZKAN TÜKEL G., Şahin B., TURHAN T.

Filomat, vol.37, no.3, pp.905-913, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2303905o
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.905-913
  • Keywords: Circle, Geodesic, Helix, Isotropic submersion, O’Neill’s tensors, Riemannian submersion, Second fundamental form
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

In this paper, when a given curve on the total manifold of a Riemannian submersion is transferred to the base manifold, the character of the corresponding curve is examined. First, the case of a Frenet curve on the total manifold being a Frenet curve on the base manifold along a Riemannian submersion is investigated. Then, the condition that a circle on the total manifold (respectively a helix) is a circle (respectively, a helix) or a geodesic on the base manifold along a Riemannian submersion is obtained. We also investigate the curvatures of the original curve on the total manifold and the corresponding curve on the base manifold in terms of Riemannian submersions.