Studies Upon an Important Geometrical Structure

摘要

In the paper herein we prove that the set T of the transformations for the coefficients of an N-linear con-nections, together with the composition of mappings isn't a group, but, we give some groups which keep invariant a part of components of the local coefficients of an N-linear connection. We determine the set of all metrical N-linear connections, in the case when the nonlinear connection is arbitrary and we consider some important par-ticular cases. We prove that the set, T~rnms_N, of the transformations of semi-symmetric metrical N-linear connections, corresponding to the same nonlinear connection N, together with the composition of mappings is a group. We obtain some important invariants of this group and we consider their properties. We also study the transformationrnlaws of the torsion tensor fields, with respect to the transformations of the group T~ms_n.