Six-dimensional considerations of Einstein's connection for the first two classes. II. The Einstein's connection in 6 - g -UFT

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2 , 3 , 4 , 5 . In the following series of two papers, we present a surveyable tensorial representation of 6 -dimensional Einstein's connection in terms of the unified field tensor: I. The recurrence relations in 6 - g -UFT. II. The Einstein's connection in 6 - g -UFT. In our previous paper [2], we investigated some algebraic structure in Einstein's 6 -dimensional unified field theory (i.e., 6 - g -UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 6 - g -UFT. This paper is a direct continuation of [2]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 6 - g -UFT and to display a surveyable tensorial representation of 6 -dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [2]. All considerations in this paper are restricted to the first and second classes of the 6 -dimensional generalized Riemannian manifold X 6 , since the case of the third class, the simplest case, was already studied by many authors.