Certain curves along Riemannian submersions
Articles > Article · 2023
Authors: Gozde Ozkan Tukel, Bayram ŞAHİN, Tunahan Turhan
FILOMAT, Journal Indexed in SCI Expanded, International, WoS, 2023, vol 37, pp 905-913
DOI: 10.2298/FIL2303905O
Summary
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.