The concept of manifold, applied to the method of Kron and justification for the Job relevance of the concept of tensors by Kron

DOI: 10.5176/2251-1911_CMCGS15.22

Authors: Philippe Durand, Olivier Maurice and Alain Reineix

Abstract:  The relevance of the approach of tensor calculus applied to objects in Kron approach was previously discussed in the day of differential geometry, mainly by authors like Lynn or Hoffmann , or Papin and Kaufmann [1]. It is proposed to revise this discussion here by approaching it with a more modern concepts related to the differentiable manifolds theory. There are interesting applications, adapted to electric machines, of concepts of special and general relativity developed by Einstein. But at first we revisit the notion of tensor given by Elie Cartan.

Keywords: Manifolds, Kron's formalism, tensorial analysis of networks, relativity