Finsler spaces with mutually opposite preferred directions and their groups of isometries

Bogoslovsky, G. Yu. (2015) Finsler spaces with mutually opposite preferred directions and their groups of isometries. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 31 (1). pp. 15-25. ISSN 0866-0174

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Abstract

It is shown that in Minkowski space there exist transformations of the coordinates of events alternative to the 3-parameter Lorentz boosts. However, in contrast to the boosts, they constitute a 3-parameter noncompact group which, in turn, is a subgroup of the homogeneous 6- parameter Lorentz group. Moreover, in the same space, there exists another 3-parameter noncompact group isomorphic to above-mentioned one. As we shall see, these two 3-parameter noncompact groups are rudiments of the 3-parameter groups of relativistic symmetry of the axially symmetric Finslerian spaces with the preferred directions ν and −ν, respectively. Finally, it will be also demonstrated that inversion of the preferred direction ν in the axially symmetric Finslerian space-time does not change the Lobachevski geometry of 3-velocity space. However, this leads to an inversion of the corresponding family of horospheres of the space.

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