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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| 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 |
| 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. |
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