Estimativa da curvatura de subvariedades limitadas

• Ano de defesa: 2018
• Autor(a) principal: Santos, Roney Pereira dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Alagoas; Brasil; Programa de Pós-Graduação em Matemática; UFAL
• Palavras-chave em Português: Geometria Riemanniana; Subvariedade limitada; Curvatura; Hessiana, função de; Geodésica; Riemannian Geometry; Limited Subvariety; Curvature; Hessian function; Geodesic; Bounded submanfiold; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://www.repositorio.ufal.br/handle/riufal/2685

In this monography, we are interested in to demonstrate the Theorem of Jorge- Koutrofiotis. For this, we use the Theorem of Omori, too demonstrated. H. Omori demonstrated that, for all complete Riemannian manifold with scalar curvature bounded below, if a differentiable function on this manifold has an upper bound, we can choose points on this manifold such that this function does not reach your supreme and the lenght of the gradient vector and the Hessian may be arbitrarily small. L. Jorge and D. Koutrofiotis as an application of the Theorem of Omori, according to which, for a complete Riemannian manifold with scalar curvature bounded below, a Hadamard manifold and an isometric immersion for the first manifold on the Hadamard manifold such that the seccional curvature of the first manifold is always smaller than the seccional curvature of the Hadamard manifold when calculated at the same points, we have that the image of the first manifold for the imersion is ilimited in the Hadamard manifold.