Estruturas não-riemannianas e a imersão do espaço-tempo em dimensões superiores

• Ano de defesa: 2012
• Autor(a) principal: Silva, Lucio Fábio Pereira da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Física; Programa de Pós-Graduação em Física; UFPB
• Palavras-chave em Português: Geometria de Weyl; Geometria de Riemann-cartan; Weyl Geometry; Riemann-Cartan Geometry; CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/5732

We consider the geometry of affine connections and take, as particular examples, Weyl and Riemann-Cartan geometies. In a modern geometrical approach, we take up the problem of local embedding of manifolds in Weyl spaces and in spaces endowed with semi-symmetric torsion. We then obtain the extrinsic curvature, Weingarten operator and Gauss-Codazzi equations in the mentioned non-riemannian spaces. We investigate some important properties of a Weyl structure in the case of a warped product and carry out an analysis of the geodesics in a foliation de…ned in such a space. We consider the particular case when the embedding space is a warped product manifold and has a Riemann-Cartan geometry. As an application, we show that the torsion …eld of de bulk may provide a mechanism of geometrical con…nement. In this way, we exhibit a classical analogue of the quantum con…nement induced by scalar …elds.