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

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