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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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2017 |
| Country: | Brasil |
| Institution: | Universidade Federal do Ceará (UFC) |
| Repository: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/27052 |
| Online Access: | http://www.repositorio.ufc.br/handle/riufc/27052 |
| Access Level: | Open access |
| Keyword: | Hipersuperfícies mínimas Curvatura de Gauss-Kronecker Curvatura escalar Minimal hypersurface Gauss-Kronecker curvature Scalar curvature |
| Summary: | 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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