Slant helices on Riemannian Manifolds

Abstract

The notion of slant helix in Euclidean space was defined by Izumiya and Takeuchi \cite{izu}, and many authors have studied such curves in Euclidean spaces. The aim of this paper is to introduce the slant helix notion on  Riemannian manifolds.  The necessary conditions for a curve on a Riemannian manifold to be a slant helix are obtained in terms of differential equations. In addition, certain conditions were found for the slant helix along an immersion to be a slant helix in the ambient space. Moreover, a criterion is given for the slant helix along an immersion to be a circle  in the ambient space (or vice versa).