Isometry classification of cubic homogeneous 3-dimensional forms

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.