Existência de conexões versus módulos projetivos

• Ano de defesa: 2013
• Autor(a) principal: Silva, Rafael Barbosa da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Conexões; Derivadas covariantes; Módulos projetivos; Seções do fibrado tangente; Connection; Covariant derivative; Projective module; Sections of the tangent bundle; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7424

The notions of connection and covariant derivative has its origin in the field of Riemannian geometry , where there is no distinction between them. In fact, in this study we found that these notions are equivalent if we consider modules over K-algebras of finite type. We also show that the existence of connections implies the existence of covariant derivative. The main goal of this study is to determine which modules admit connections. We easily verified that the projective modules admit connections. In fact, they form an affine space. But we also display a module that is not projective and has connection. Later, inspired by Swan's theorem, we explore in a straightforward way modules formed by sections of the tangent bundle of some surfaces in 3-dimensional real space. Finally, we study the notion of connection introduced by Alain Connes in modules over K-algebras not necessarily commutative. And we find in that context that the modules that have connection are exactly the projectives modules.