Parametrizations of minimal timelike surfaces in the four-dimensional pseudo-Euclidean space of index two

TL;DR

This paper develops explicit representation formulas for minimal timelike surfaces in four-dimensional pseudo-Euclidean space of index two, enabling their construction without integration and providing new examples of such surfaces.

Contribution

It introduces novel parametrization formulas for minimal timelike surfaces in pseudo-Euclidean spaces, including a special case involving integration in three dimensions.

Findings

Representation formulas for local null curves in 4D pseudo-Euclidean space of index two.

Explicit parametrizations for minimal timelike surfaces without integration.

Examples of minimal timelike surfaces derived from the formulas.

Abstract

We construct representation formulas for local null curves in the four-dimensional pseudo-Euclidean space of index two and derive corresponding parametrizations for local minimal timelike surfaces without integration. As a special case of the representation formula, we construct a representation formula for local null curves in the three-dimensional pseudo-Euclidean space of index one that involves integration. Our results provide examples of minimal timelike surfaces.