Bour's spacelike maximal and timelike minimal surfaces in the 3-dimensional Minkowski space

TL;DR

This paper explores Bour's surfaces in 3D Minkowski space, analyzing their properties as spacelike maximal and timelike minimal surfaces through Weierstrass representations.

Contribution

It characterizes the definite and indefinite cases of Bour's surfaces and investigates their differential geometric properties in Minkowski space.

Findings

Identification of definite and indefinite cases of Bour's surfaces.

Derivation of Weierstrass representations for these surfaces.

Analysis of geometric properties of maximal and minimal surfaces.

Abstract

Bour's minimal surface has remarkable properties in three dimensional Minkowski space. We reveal the definite and indefinite cases of the Bour's surface using Weierstrass representations, and give some differential geometric properties of the astonishing maximal and minimal surfaces.