Certain curves along Riemannian submersions
Filomat, vol.37, no.3, pp.905-913, 2023 (SCI-Expanded, Scopus)
- 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, zbMATH
- Page Numbers: pp.905-913
- Keywords: Circle, Helix, Geodesic, Riemannian submersion, O?Neill?s tensors, Second fundamental form, Isotropic submersion, ISOTROPIC IMMERSIONS, MANIFOLDS, SPACE
- Süleyman Demirel University Affiliated: Yes
Abstract
© 2023, University of Nis. All rights reserved.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.