MATHEMATICAL STRUCTURE FOR A FIVE DIMENSIONAL CARTAN THEORY OF SPACE-TIME

Manoel Ferreira BORGES[1]

§    ABSTRACT: The main purpose of this article is the construction of a mathematical structure for a five dimensional extended Cartan gravity theory. From a brief review of E. Cartan's Mathematical related to the connection and curvature on a manifold, Cartan gravity theory is outlined. The criterion followed for its construction represents in many ways an extensions of some concepts and consequences reported in an early reference by D'Auria et al.(1981), such as: (i) the pseudo-connection or potential m A , which is an extension of the original Cartan connection; (ii) Rheonomy, a generalized symmetry, here regarded as underlying the whole structure of the group-manifold, and not being a simple consequence arising out of the variational principle.

§    KEYWORDS: Cartan Theory; manifold; space-time; connection; curvature.

 



[1]Assittant professor - Departamento de Ciências da Computação e Estatística - Instituto de Biociências, Letras e Ciências Exatas - UNESP - 15054-000 São José do Rio Preto - SP - Brasil.