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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.

##### MSC:
 53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
##### Keywords:
connections; main scalars; Finsler space; $$m$$-th root metric