A New Approach on Helices in Pseudo-Riemannian Manifolds

Abstract

A proper curve $\alpha$ in the $n$-dimensional pseudo-Riemannian manifold $(M,g)$ is called a $V_n$-slant helix if the function $g(V_n,X)$ is a nonzero constant along $\alpha$, where $X$ is a parallel vector field along $\alpha$ and $V_n$ is $n$th Frenet frame. In this work, we study such curves and give important characterizations about them.