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

Abstract

Einstein's connection in a generalized Riemannian manifold Xn has been investigated by many authors for lower-dimensional cases n=2,…,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 X7. 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 Xn. 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.