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.
Lower dimensional cases of Einstein's connection were already investigated by many authors forn=2,3,4,5. In the following series of two papers, we present a surveyable tensorial representation of6-dimensional Einstein's connection in terms of the unified field tensor:I. The recurrence relations in6-g-UFT.II. The Einstein's connection in6-g-UFT.In our previous paper [2], we investigated some algebraic structure in Einstein's6-dimensional unified field theory (i.e.,6-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in6-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 in6-g-UFT and to display a surveyable tensorial representation of6-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 the6-dimensional generalized Riemannian manifoldX6, since the case of the third class, the simplest case, was already studied by many authors.
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