A note on pairs of metrics in a three-dimensional linear vector space

TL;DR

This paper classifies pairs of metrics in a 3D linear space, focusing on Minkowski-type metrics with signature (+,-,-), and provides canonical forms for each class.

Contribution

It introduces a classification scheme for metric pairs in three-dimensional space and offers canonical representations for each class, enhancing understanding of their structure.

Findings

Classification of metric pairs into distinct classes

Canonical forms for each class of metric pairs

Insight into Minkowski-type metric pair structures

Abstract

Pairs of metrics in a three-dimensional linear vector space are considered, one of which is a Minkowski type metric with the signature (+,-,-). Such metric pairs are classified and canonical presentations for them in each class are suggested.