Geometria extrínseca de campos de vetores em R3

• Ano de defesa: 2016
• Autor(a) principal: Gomes, Alacy José
• Orientador(a): Garcia, Ronaldo Alves
• Banca de defesa: Garcia, Ronaldo Alves, Tello, Jorge Manuel Sotomayor, Mello, Luis Fernando de osorio, Tari, farid, Carneiro, Mario Jorge Dias
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Matemática (IME)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Campos de vetores; Distribuição de planos; Equações diferenciais implícitas; Pontos parcialmente umbílicos; Linhas principais
• Palavras-chave em Inglês: Vector fields; Plane distribution; Implicit differential equations; Partially umbilic points; Principal lines
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/8636

In this work we first consider regular vector fields : R3 ! R3 and its orthogonal distribution of planes. We present a characterization of the normal curvature associated to and the system of implicit differential equations 2(D (dr); dr; ) + h rot( ); i hdr; dri = 0; hdr; i = 0; which define two one-dimensional singular and orthogonal foliations, which we call by principal foliations and whose leaves are the principal lines of the distribution . Next we describe the configurations of the principal foliations in a neighborhood of the generic singular points that constitutes a regular curve in R3, which are denoted by Darbouxian umbilic partially points and semi-Darbouxian. We proceed by studying the stability of the closed principal lines and we also present a Kupka- Smale genericity result. To conclude, we study the structure of the singularities of the principal foliations in a neighborhood of a singular hyperbolic point of the vector field .