Abstract
Defines torsion and curvature as appropriate to the generalized non-Riemannian geometry first used in 1925 by Einstein for his unified field theory and recently shown to constitute the algebraic extension of general relativity over the algebra of hypercomplex numbers. The author stresses the fact that the Riemannian definitions are not appropriate on the base manifold. Fundamental notions of this generalized geometry are presented without reference to the bundle of frames as a simpler, more direct approach. The new definitions prove to be illuminating for the understanding of the geometry and all its potential applications. They have not been considered previously and show in particular that is the usual case there is in fact no torsion.
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