Superfícies em R4 do ponto de vista da teoria das singularidades
We study the geometry of surfaces immersed in R4 through the singularities of their families of height functions. Inflection points on the surfaces are shown to be umbilic points from their families of height functions. Furthermore, we see that inflection points of imaginary type are isolated points...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Brasil |
| Recursos: | Universidade Federal da Paraíba (UFPB) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da UFPB |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufpb.br:tede/7447 |
| Acesso em linha: | https://repositorio.ufpb.br/jspui/handle/tede/7447 |
| Access Level: | acceso abierto |
| Palavra-chave: | Singularidades Segunda forma fundamental Elípse de curvatura Ponto de inflexão Mergulho genérico Singularities Second fundamental form Ellipse curvature Height function Inflexion point Umbílic point Embedding generic Função altura Ponto umbílico CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Resumo: | We study the geometry of surfaces immersed in R4 through the singularities of their families of height functions. Inflection points on the surfaces are shown to be umbilic points from their families of height functions. Furthermore, we see that inflection points of imaginary type are isolated points of the curve --1(0). As a consequence we prove that any dive generic convexly embedded S2 in R4 has inflexion points. |
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