Construção de superfícies utilizando o Teorema de Poincaré

• Autor(a) principal: Oliveira Júnior, João de Deus
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://locus.ufv.br/handle/123456789/4901
• topic: Geometria hiperbólica; Grupos Fuchsianos; Emparelhamento de arestas de polígonos; Superfícies de Riemenn; Hyperbolic geometry; Groups fuchsianos; Pairings of edges of polygons; Surfaces Riemann; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA

This study deals with the surface of the compact quotient M2=G where the surface M2 is either the Euclidean plane or the plane spherical or the hyperbolic plane, G is a group of isometries of their surfaces, and this group is generated by matching of edges of polygons. The Poincaré theorem that provides a method of finding the group of isometries G the functions that the pair of edges of the polygons involved. By using this theorem we construct two new pairings of generalized edges (Chapter 4) associated with the tessellations {12η 8,4} e {12μ 12,4}, respectively. These tessellations provide packing of spheres whose packing density is very close to the maximum 3/π. Such pairings are the starting point for finding codes with optimal transmission rates for Multiple-Input Multiple-Output (MIMO).