Hipersuperfícies mínimas de R4 com curvatura de Gauss-Kronecker nula.

This work does study the complete minimal hypersurfaces in the Euclidean space R4 , with Gauss-Kronecker curvature identically zero. Our main result is to prove that if f: M3 → R4 is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental...

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Detalles Bibliográficos
Autor: Pereira, José Ilhano da Silva
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Federal do Ceará (UFC)
Repositorio:Repositório Institucional da Universidade Federal do Ceará (UFC)
Idioma:portugués
OAI Identifier:oai:repositorio.ufc.br:riufc/27052
Acceso en línea:http://www.repositorio.ufc.br/handle/riufc/27052
Access Level:acceso abierto
Palabra clave:Hipersuperfícies mínimas
Curvatura de Gauss-Kronecker
Curvatura escalar
Minimal hypersurface
Gauss-Kronecker curvature
Scalar curvature
Descripción
Sumario:This work does study the complete minimal hypersurfaces in the Euclidean space R4 , with Gauss-Kronecker curvature identically zero. Our main result is to prove that if f: M3 → R4 is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature boun-ded from below, then f(M3) splits as a Euclidean product L2 × R , where L2 is a complete minimal surface in R3 with Gaussian curvature bounded from below. Moreover, we show a result about the Gauss-Kronecker curvature of f, without any assumption on the scalar curvature.