Hipersuperfícies Levi-flat e webs holomorfas

• Ano de defesa: 2021
• Autor(a) principal: Ayane Adelina da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE MATEMÁTICA; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: Folheações Holomorfas; Webs Holomorfas; Hipersuperfícies Levi-flat; Matemática – Teses; Folheações Holomorfas – Teses; Webs holomorfas – Teses; Hipersuperfícies Levi-flat – Teses
• Link de acesso: http://hdl.handle.net/1843/45071; https://orcid.org/ 0000-0003-1911-9303

In this thesis, aspects of the local and global theory of Holomorphic Webs and Levi-flat Hypersurfaces will be considered. We will address three proposals. The first one, is to consider a real analytic Levi-flat hypersurface induced by a real analytic curve in the Grassmanian of complex hyperplanes. We will prove that Levi’s foliation associated with this hypersurface extends to a holomorphic web. The second one is to study conditions sufficient for the existence of singularities with local first integral of a web on a compact complex surface which leave invariant a real analytic Levi-flat hypersurface. Finally, the third one is the study of real analytic hypersurfaces associated to real analytic maps that satisfy the conditions of Milnor fibration. We will see that under certain conditions that such hypersurfaces are not Levi-flat.