Eikonal Helices and Harmonic Curvatures in Riemannian Manifolds

In this paper, we define eikonal helix curves and eikonal Vn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{n}$$\end{document}-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 Vn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{n}$$\end{document}-slant helix curves in an n-dimensional Riemannian manifold. Moreover, we give conclusions for eikonal helix curves and eikonal Vn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{n}$$\end{document}-slant helix curves by making use of the harmonic curvature functions.