On the group of transformations of symmetric conformal metrical N-linear connections on a Hamilton space of order k

Abstract

In the present paper, we obtain in a Hamilton space of order k the transformation laws of the torsion and curvature tensor fields, with respect to the transformations of the group T_N of the transformations of N−linear connections having the same nonlinear connection N. We also determine in a Hamilton space of order k the set of all metrical semisymmetric N−linear connections, T^ms_N, in the case when the nonlinear connection is fixed and we prove that T^ms_N, together with the composition of mappings’s a group. We obtain some important invariants of group T^ms_N and give their properties. We also study the transformation laws of the torsion d−tensor fields with respect to the transformations of the group T^ms_N.