Soluções invariantes para o tensor de Schouten e tensor curvatura prescritos em variedades localmente conformemente planas

• Autor(a) principal: Carvalho, Marcos Tulio Alves de
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000007kxm
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/8635
• topic: Tensor de Schouten; Operador curvatura; Schouten tensor; Curvature operator; MATEMATICA::GEOMETRIA E TOPOLOGIA

In this work we study two problems: the first one involving the prescribed Schouten tensor and the second one the prescribed curvature operator. The first problem was inspired by the works Deturck and Yang, [6], which consist of: Given a tensor T of order 2 in the pseudo-Euclidean space ( ,g), n ≥ 3, with coordinates x = ( ), and metric g, where , = ±1, find a metric as = g, such that the tensor of Schouten be T. The second problem is the problem of the prescribed curvature tensor consist of: Let Euclidean space ( ;g), n ≥ 3, with coordinates x = ( ), is , the R a tensor of order 4 of the form , where T = , with differentiable functions.We want to find a metric = g, such that = , where is the tensor curvature of the metric . Considering that the solutions are invariant by translation and rotation, we find necessary and sufficient conditions for both problems to have solution.