On f-Eikonal Helices And f-Eikonal Slant Helices In Riemannian Manifolds

TL;DR

This paper introduces new classes of curves called f-eikonal helix and V_{n}-slant helix in Riemannian manifolds, along with their harmonic curvature functions, providing characterizations that extend the understanding of geometric structures in such manifolds.

Contribution

It defines f-eikonal helix and V_{n}-slant helix curves and their harmonic curvature functions, offering new characterizations in Riemannian geometry.

Findings

Defined f-eikonal helix and V_{n}-slant helix curves.

Established characterizations using harmonic curvature functions.

Extended geometric understanding of curves in Riemannian manifolds.

Abstract

In this paper, we define f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Also, we give the definition of harmonic curvature functions related to f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Moreover, we give characterizations for f-eikonal helix curves and f-eikonal V_{n}-slant helix curves by making use of the harmonic curvature functions.