Generalized Bour's theorem in Minkowski 3-space

TL;DR

This paper extends Bour's theorem to Minkowski 3-space, constructing isometric minimal helicoidal and rotational surfaces and analyzing their properties under Gauss map conditions.

Contribution

It introduces a generalized version of Bour's theorem in Minkowski space, enabling the creation of minimal helicoidal and rotational surfaces with preserved minimality.

Findings

Constructed isometric minimal helicoidal surfaces.

Constructed isometric minimal rotational surfaces.

Proved minimality preservation under Gauss map conditions.

Abstract

We obtain isometric minimal helicoidal and rotational surfaces using generalized Bour's theorem in three dimensional Minkowski space. In addition, we show that the surfaces preserve minimality when their Gauss maps identically equal, choosing any diffentiable functions on the profile curve.