N-Legendre and N-Slant Curves in the Unit Tangent Bundle of Minkowski Surfaces

TL;DR

This paper extends the study of N-Legendre and N-slant curves to the unit tangent bundle of Minkowski surfaces, providing new characterizations within the pseudo-Riemannian geometric framework.

Contribution

It introduces the analysis of N-Legendre and N-slant curves in Minkowski surfaces' tangent bundles, expanding prior work to a pseudo-Riemannian setting and offering new geometric characterizations.

Findings

Characterizations of N-Legendre curves in Minkowski tangent bundles

Characterizations of N-slant curves in Minkowski tangent bundles

Extension of previous Euclidean results to Minkowski geometry

Abstract

Let $(\mathbb{M}_{1}^{2},g)$ be a Minkowski surface and $(T_1\mathbb{M}_1^2, g_1)$ its unit tangent bundle endowed with the pseudo-Riemannian induced Sasaki metric. We extend in this paper the study of the N-Legendre and N-slant curves which the inner product of normal vector and Reeb vector is zero and nonzero constant respectively in $\left( T_1 \mathbb{M}_1^2, g_1 \right)$, given in \cite{hmy}, to the Minkowski context and several important characterizations of these curves are given.\newline