AbstractContinuing 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 groupsSU(2) andSU(2