Eikonal Helices and Harmonic Curvatures in Riemannian Manifolds

Abstract

In this paper, we define eikonal helix curves and eikonal \(V_{n}\)-slant helix curves in an n-dimensional Riemannian manifold. In addition, we give the definition of harmonic curvature functions related to eikonal helix curves and eikonal \(V_{n}\)-slant helix curves in an n-dimensional Riemannian manifold. Moreover, we give conclusions for eikonal helix curves and eikonal \(V_{n}\)-slant helix curves by making use of the harmonic curvature functions.