Geodesic
Certain curves along Riemannian submersions
Filomat, Tome 37 (2023) no. 3, p. 905

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DOI

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.
DOI : 10.2298/FIL2303905O
Classification : 53B20, 58D17
Keywords: Circle, Helix, Geodesic, Riemannian submersion, O’Neill’s tensors, Second fundamental form, Isotropic submersion 
Gözde Özkan Tükel; Bayram Şahin; Tunahan Turhan. Certain curves along Riemannian submersions. Filomat, Tome 37 (2023) no. 3, p. 905 . doi: 10.2298/FIL2303905O
@article{10_2298_FIL2303905O,
     author = {G\"ozde \"Ozkan T\"ukel and Bayram \c{S}ahin and Tunahan Turhan},
     title = {Certain curves along {Riemannian} submersions},
     journal = {Filomat},
     pages = {905 },
     year = {2023},
     volume = {37},
     number = {3},
     doi = {10.2298/FIL2303905O},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2303905O/}
}
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