On Cartan Spaces with the $m$-th Root Metric $K(x,p)=\sqrt[m]{a^{i_{1}i_{2}...i_{m}}(x)p_{i_{1}}p_{i_{2}}...p_{i_{m}}}$

Abstract

The aim of this paper is to expose some geometrical properties of the locally Minkowski-Cartan space with the Berwald-Moor metric of momenta. This space is regarded as a particular case of the $m$-th root Cartan space. Thus, Section 2 studies the $v$-covariant derivation components of the $m$-th root Cartan space. Section 3 computes the $v$-curvature d-tensor $S^{hijk}$ of the m-th root Cartan space and studies conditions for $S3$-likeness. Section 4 computes the $T$-tensor $T^{hijk}$ of the m-th root Cartan space. Section 5 particularizes the preceding geometrical results for the Berwald-Moor metric of momenta.