A new approach on helices in pseudo-Riemannian manifolds

TL;DR

This paper introduces a new type of helix called V_{n}-slant helix in n-dimensional pseudo-Riemannian manifolds, along with characterizations and definitions related to harmonic curvature functions.

Contribution

It defines V_{n}-slant helix and harmonic curvature functions in pseudo-Riemannian manifolds, providing new theoretical insights into their properties.

Findings

Defined harmonic curvature functions in terms of V_{n}

Introduced V_{n}-slant helix in pseudo-Riemannian manifolds

Provided characterizations of the new helix type

Abstract

In this paper, we give a definition of harmonic curvature functions in terms of V_{n} and define a new kind of slant helix which is called V_{n}-slant helix in n-dimensional pseudo-Riemannian manifold. Also, we give important characterizations about the helix.