Examples of Finslerian Metric Tensors of the Space-Time Signature

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Abstract

Continuing the previous work [1], where a way of associating the gauge fields with Finslerian metrics has been indicated, in the present note we propose a class of Finslerian metrics which are of interest for the following two reasons. Firstly, the metrics give rise to the Finslerian metric tensors of the space-time signature (+ − − −). Secondly, the associated indicatrices prove to be spaces of constant curvature, yielding examples of the Finslerian metrics which reflect the internal symmetry groups SU(2) and SU(2)⊗SU(2).

Abstract

Beispiel für Finslerische Metriken mit Raum-Zeit-Signatur

Es werden Finslerische Metriken mit Lorentzscher Signatur angegeben, die Verallgemeinerungen von allgemein-relativistischen Riemannschen Räumen konstanter Krümmung sind und die die Gruppen SU(2) bzw. SU(2) × SU(2) als innere Symmetrien enthalten.

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