On the natural lift curves for the Involute spherical indicatrices in Minkowski 3-space

TL;DR

This paper investigates the conditions under which natural lift curves of spherical indicatrices of involutes in Minkowski 3-space are integral curves of the geodesic spray, providing criteria and examples.

Contribution

It introduces new criteria for natural lift curves of involute spherical indicatrices to be integral curves in Minkowski 3-space, with specific results on spacelike evolutes and Darboux vectors.

Findings

Criteria for natural lift curves to be integral curves

Results on spacelike evolute curves with timelike binormal

Illustrative example of main results

Abstract

The aim of this paper is to determine criteria of being integral curve for the geodesic spray of the natural lift curves of the spherical indicatrices of the involutes of a given spacelike curve with a timelike binormal in Minkowski 3-space. Furthermore, some interesting results about the spacelike evolute curve with timelike binormal and spacelike or timelike Darboux vector were obtained, depending on the assumption that the natural lift curves of the spherical indicatrices of the involute curve should be the integral curve on the tangent bundle. Additionally we illustrate an example of our main results.