About the group of transformations of metrical semisymmetric N−linear connections on a generalized Hamilton space of order two

Abstract

In the present paper, we obtain in a generalized Hamilton space of order two the transformation laws of the torsion and curvature tensor fields, with respect to the transformations of the group T_Nof the transformations of N−linear connections having the same nonlinear connection N. We also determine in a generalized Hamilton space of order two the set of all metrical semisymmetric N−linear connections, in the case when the nonlinear connection is fixed and prove that this set, T^ms_N of the transformations of metrical semisymmetric N−linear connections, having the same nonlinear connection N, together with the composition of mappings, is a group. We obtain some important invariants of the group ms T^ms_N and give their properties. We also study the transformation laws of the torsion d−tensor fields with respect to the transformation of the group ms T^ms_N.