Six-dimensional considerations of Einstein's connection for the first two-classes. I: The recurrence relations in 6-\(g\)-UFT (Q1587803)

Summary: 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.