THE CONSTRUCTION OF TELEPARALLEL FINSLER CONNECTIONS AND THE EMERGENCE OF AN ALTERNATIVE CONCEPT OF METRIC COMPATIBILITY

The issue of whether teleparallel nonlinear connections exist is resol ved by their explicit construction on Finslerian metrics that arise in the Robertson test theory of special relativity (RTTSR), and on the M inkowski metric in particular. The method is an adaptation to the Fins ler bundle of a similar construction for teleparallel linear connectio ns. It suggests the existence of a concept of metric compatibility alt ernative to omega(mu lambda) + omega(lambda mu) = 0 for teleparallel n onlinear connections. A sophisticated system of partial differential e quations whose solutions have been discussed in the computing literatu re is interpreted in geometric terms. The characteristics of the solut ions are checked against compliance with the condition omega(mu lambda ) + omega(lambda mu) = 0, an issue whose relevance for this theory der ives from the fact that nonantisymmetric connections repeatedly appear in teleparallel geometry.