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Six-dimensional considerations of Einstein’s connection for the first two-classes. I: The recurrence relations in 6-\(g\)-UFT. (English) Zbl 0981.83060

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.

MSC:

83E50 Supergravity
53Z05 Applications of differential geometry to physics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
58A05 Differentiable manifolds, foundations
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