Hipersuperfícies de curvatura média constante folheadas por esferas

• Autor(a) principal: Butta, André Pizzaia
• Data de Publicação: 2008
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal de Alagoas (UFAL)
• Texto Completo: http://www.repositorio.ufal.br/handle/riufal/5570
• topic: Geometria diferencial; Hipersuperfícies; Folheação (Matemática); Curvatura media; Differential geometry; Hypersurfaces; Foliage (Mathematics); Medium curvature; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This MSc will explore hypersurfaces n-dimensional (lines) in Euclidean space Rn +1 and in the hyperbolic space Hn +1. Consider that the hypersurfaces have constant mean curvature and are plated by (n-1)-hyperspheres. We will need results classics as Alexandrov's theorem and a theorem of symmetry. Basically answer the following question: When a hypersurface of dimension n with constant mean curvature and sliced by a ball in the space above is a hypersurface of revolution? Moreover, in Rn +1 the spheres will be contained in parallel hyperplanes and in horoesferas Hn +1.