On the Spherical Indicatrices of a Timelike Curve as Generalized Helices in Minkowski 3-Space

Abstract

In the present paper, we investigate new properties of the spherical indicatrices of a timelike curve in Minkowski 3-space $\mathbb{E}_1^3$. We focus on the conditions of the spherical indicatrix to be a generalized helix depending on its causal character. We also give some integral equations by defining the axis of the helix in the means of the local frame.