Isometry classification of cubic homogeneous 3-dimensional forms

TL;DR

This paper classifies cubic homogeneous 3D Finsler metrics based on their isometry groups, identifying six affine types and exploring the relationship between symmetries and projective classifications.

Contribution

It introduces a classification of cubic homogeneous 3D Finsler metrics into six affine types and analyzes their isometry algebras and symmetry properties.

Findings

Six distinct affine types of cubic homogeneous 3D Finsler metrics identified.

Isometry algebras characterized and related to affine-invariant properties.

Discussion of the connection between symmetries and projective classifications.

Abstract

The problem of classification of cubic homogeneous Finslerian 3D metrics with respect to their isometries is considered. It is shown, that there are 6 different general affine types of such metrics. Algebras of isometries are presented in apparent kind together with their affine-invariant properties. Interrelation between symmetries and projective classifyings is discussed.