Abstract

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 X6, since the case of the third class, the simplest case, was already studied by many authors.