Three- and five-dimensional considerations of the geometry of Einstein's* g-unified field theory

We study the algebraic and differential geometric structures of three- and five-dimensional^* g-unified field theory, with emphasis on the five-dimensional^* g-unified field theory, in which we derive a new set of powerful recurrence relations which hold in a five-dimensional generalized Riemannian manifoldX ₅ , prove a necessary and sufficient condition for the existence and uniqueness of the solution of the system of the Einstein equations in the first two classes, and find a precise tensorial representation of the Einstein connection in terms of^*g .