The main scalar of two-dimensional Finsler spaces with special metric (Q2367104)

In a two-dimensional Finsler space \(F^ 2=(M,F)\) the Berwald frame \((l,m)\) and its moving equations are considered. The author introduces the main scalar \(I\) [see the author, Foundations of Finsler geometry and special Finsler spaces (Japan 1986; Zbl 0594.53001)] of the space \(F^ 2\). The main scalar \(I\) is studied for some spaces \(F^ 2\) with the special metrics in relations to the indicatrix. So are given the important results about: a theorem of classification of Berwald spaces \(F^ 2\) with \(l\)-form metric; spaces \(F^ 2\) with \(I \neq 0\); the Finsler metric defined by a quite normal indicatrix; and the main scalar of Wrona's metric.