Seven-dimensional considerations of Einstein's connection. I: The recurrence relations of the first kind in \(n\)-\(g\)-UFT (Q1864313)

Summary: Einstein's connection in a generalized Riemannian manifold \(X_n\) has been investigated by many authors for lower-dimensional cases \(n=2,\dots ,6\). In a series of papers, we obtain a surveyable tensorial representation of \(7\)-dimensional Einstein's connection in terms of unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in \(X_7\). In this paper, we give a brief survey of Einstein's unified field theory and derive the recurrence relations of the first kind which hold in a general \(X_n\). All considerations in this paper 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.