## 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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