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Conexões afins e a teoria de Cartan-Einstein
(Universidade Federal do Espírito Santo, 2016-07-12) Xavier, Roberta Meschese; Câmara, Leonardo Meireles; Macarini, Leonardo Magalhães; Vieira, Matheus Brioschi Herkenhoff
The Cartan-Einstein theory of gravitation is a modified version of the General Theory of Relativity. While Einstein’s theory was developed according to the hypothesis that the relativity of space-time has zero torsion, Cartan allows torsion and relate it to the angular momentum of the matter several years before the discovery of the spin of the electron. Cartan’s articles, in particular Sur les variétés the affine connexion et la théorie de la Généralisée relativité, which is the basis of this work, contains important new mathematical ideas that have influenced the development of differential geometry and, in particular, led to the general theory of affine connections. Essentially these are geometrical objects on a differentiable manifolds that connect nearby tangent spaces. In this dissertation we study the invariance of the laws of classical and relativistic mechanics in continuous media and the geometry of space-time from the standpoint of affine connections.