Surface family with a common natural asymptotic lift of a timelike curve in Minkowski 3-space

TL;DR

This paper introduces a family of surfaces in Minkowski 3-space where the natural lift of a timelike curve acts as an asymptotic, providing conditions and examples for such geometric configurations.

Contribution

It establishes necessary and sufficient conditions for the natural lift of a timelike curve to be an asymptotic on surfaces in Minkowski 3-space, expanding geometric understanding.

Findings

Conditions for natural lifts to be asymptotic

Explicit examples of such surfaces

Method for constructing these surfaces

Abstract

In the present paper, we find a surface family possessing the natural lift of a given timelike curve as a asymptotic in Minkowski 3-space. We express necessary and sufficient conditions for the given curve such that its natural lift is a asymptotic on any member of the surface family. Finally, we illustrate the method with some examples.