Abstract

Lower dimensional cases of Einstein's connection were already investigated by many authors for n=2,3,4,5. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 6-dimensional Einstein's connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 6-dimensional Einstein's unified field theory (i.e., 6-g-UFT):I. The recurrence relations in 6-g-UFT.II. The Einstein's connection in 6-g-UFT.All considerations in these papers are restricted to the first and second classes only, since the case of the third class, the simplest case, was already studied by many authors.