Bonnet pairs of surfaces in Minkowski space

TL;DR

This paper investigates the local classification of Bonnet pairs of surfaces in Minkowski space using split quaternions, extending methods from Euclidean space to a Lorentzian setting.

Contribution

It introduces a novel approach employing split quaternions for classifying Bonnet pairs in Minkowski space, expanding the geometric understanding in Lorentzian geometry.

Findings

Classification results for Bonnet pairs in Minkowski space

Application of split quaternions to Lorentzian surface theory

Extension of Euclidean methods to Minkowski geometry

Abstract

In this note we consider the problem of local classification of Bonnet pairs of surfaces in 3-dimensional Minkowski space. We use split quaternions in a way similar to the use of quaternions in, arXiv:dg-ga/9610006, for the solution in Euclidean 3-Space.