Sobre a Geometria de Imersões Riemannianas

• Ano de defesa: 2015
• Autor(a) principal: Santos, Fábio Reis dos Santos
• Tipo de documento: Tese
• 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: Variedades localmente simétrica; Locally symmetric manifolds; Subvariedades Weingarten lineares; Hipersuperfícies totalmente umbílicas; Hipersuperfícies isoparamétricas; Subvariedades tipo-espaço; Steady state space; Linear Weingarten submanifold; Totally umbilical hypersurfaces; Isoparametric hypersurfaces; Spacelike submanifolds; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/8031

Our purpose is to study the geometry of Riemannian immersions in certain semi- Riemannian manifolds. Initially, considering linearWeingarten hypersurfaces immersed in locally symmetric manifolds and, imposing suitable constraints on the scalar curvature, we guarantee that such a hypersurface is either totally umbilical or isometric to a isoparametric hypersurface with two distinct principal curvatures, one of them being simple. In higher codimension, we use a Simons type formula to obtain new characterizations of hyperbolic cylinders through the study of submanifolds having parallel normalized mean curvature vector field in a semi-Riemannian space form. Finally, we investigate the rigidity of complete spacelike hypersurfaces immersed in the steady state space via applications of some maximum principles.