Um estudo da geometria projetiva elíptica

• Ano de defesa: 2015
• Autor(a) principal: Andrade, Andréa Ferreira Faccioni de [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Geometry, Projective; Geometria projetiva; Geometria riemaniana; Geometria não-euclidiana; Euler, Teorema de
• Link de acesso: http://hdl.handle.net/11449/134030; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/12-01-2016/000857275.pdf

We have made a study of projective elliptic geometry based on the book Introdução à Geometria Projetiva of Abdênago Alves de Barros and Plácido Francisco de Assis Andrade. In order to introduce this theme in a didactic way, we developed some topics of the linear algebra and of the analytic geometry, that will be used in this work. The projective elliptic geometry is divided in two approaches the double elliptic geometry and the simple elliptic geometry. The double elliptic geometry has as model the unit sphere S2 and the simple elliptic geometry has as model the real projective plane RP2; that is, the unit sphere S2 with the equivalence relation that identi es antipodal points