Theory of Finsler spaces with \(m\)-th root metric: Connections and main scalars. (English) Zbl 0843.53017

The authors study connections and main scalars of a Finsler space with \(m\)-th root metric. The paper consists of two parts. In the first part, the nonlinear connection of the Berwald connection, the Cartan connection and geometrics of a Finsler space with \(m\)-th root metric is given by \(m\)-th order Christoffel symbol and special tensor fields which are defined by \(m\)-th root Finsler metric. In the second part the authors’ considerations is restricted to the two-dimensional case and the main scalars of a cubic and quadric metric are given.


53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)