Um estudo sobre a curvatura escalar e curvatura média de ordem superior de hipersuperfícies tipo-espaço em espaços-tempos GRW

• Ano de defesa: 2022
• Autor(a) principal: Moura, Paulo Vicente Correia de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Espaço-tempo Robertson-Walker generalizado; Curvatura de ordem superior; Curvatura escalar; Fórmulas integrais tipo-Minkowski; Generalized Robertson-Walker space-time; Higher order curvature; Scalar curvature; Minkowski-type integral formulas; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/23376

In this work, we obtain new results for a space-like hypersurface immersed in a generalized Robertson-Walker spacetime (GRW) to be a slice, under the assumption of higher-order average curvature. For this, we calculate the operator Lk acting on the height function h and on the function ⟨N,K⟩. Using the formula found for the operator Lk acting on the height function, we were able to develop successive Minkowski-type integral formulas for compact space-like hypersurfaces immersed in a GRW spacetime, which are essential tools to obtain and extend results from uniqueness to such hypersurfaces in the GRW. In a second moment, we study the scalar curvature of space-like hypersurfaces immersed in an arbitrary GRW space-time and then apply the results obtained to understand the behavior of the scalar curvature of space-like hypersurfaces immersed in space-time. More specific GRWs, like the Einsteins and Parabolics.