Solitons de Ricci e métricas quasi-Einstein em variedades homogêneas

• Ano de defesa: 2013
• Autor(a) principal: Silva Filho, João Francisco da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Geometria riemaniana; Variedades riemanianas; Variedades homogêneas; Solitons de Ricci; Métricas quasi-Einstein
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/7291

The purpose of this work is study Ricci solitions and quasi-Einstein metrics on simply connected homogeneous Riemannian manifolds, with emphasis in problems in three and four dimensions, trying to characterize and to describe explicitly such structures, getting results of existence, uniqueness and consequently, build new examples on these class of manifolds. The quoted description consists basically in to obtain conditions that ensure the existence and show explicitly the family of vector fields that generate each of these structures, relating them identifying what of these vector fields are gradient. We should highlight that in the part of this work that corresponds to homogeneous three manifolds, we will consider the classification relative to dimension of isometry group, while in the part that corresponds to homogeneous four manifolds, we treat only the solvable geometry Lie type, namely, the simply connected solvable Lie group with left invariants metrics.