Study of some curves along conformal submersion

Abstract

In this article, we study bi-f-harmonic curves, hyperelastic curves, helices and circles along conformal Riemannian submersion. We investigate the behavior of an arbitrary horizontal curve on the total manifold under the conformal submersion. Moreover, we show that a totally geodesic Riemannian submersion takes a horizontal bi-f-harmonic curve, helix and circle to a bi-f-harmonic curve, helix and circle on target manifold, respectively. In addition, we also find the conditions for which Riemannian submersion takes a horizontal bi-f-harmonic curve, helix and circle to a bi-f-harmonic curve, helix and circle on target manifold, respectively.