Pontos axiumbílicos de superfícies imersas em R4
The notion of umbilic points and principal curvature lines are traditionally studied in surfaces of R3. Our goal is to extend these notions to surfaces immersed in R4. For this, we will analyze the image of the second fundamental form, restricted to the unit circle in the normal plane of the surface...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Brasil |
| Recursos: | Universidade Federal de Sergipe (UFS) |
| Repositorio: | Repositório Institucional da UFS |
| Idioma: | portugués |
| OAI Identifier: | oai:oai:ri.ufs.br:repo_01:riufs/5821 |
| Acesso em linha: | https://ri.ufs.br/handle/riufs/5821 |
| Access Level: | acceso abierto |
| Palavra-chave: | Matemática Superfícies (matemática) Curvatura Elipse (geometria) Elipse de curvatura Pontos axiumbílicos Linhas de curvatura axiais Ellipse of curvature Axiumbilics points Axial curvature lines CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Resumo: | The notion of umbilic points and principal curvature lines are traditionally studied in surfaces of R3. Our goal is to extend these notions to surfaces immersed in R4. For this, we will analyze the image of the second fundamental form, restricted to the unit circle in the normal plane of the surface. We show that this image is an ellipse, called ellipse of curvature. The points where the ellipse of curvature becomes a circle are called axiumbilics points and lines corresponding to large and small axes of the ellipse are called, respectively, of principal and mean axial lines. In this work we describe the structure of the principal axial lines on surfaces immersed in R4 in the neighborhood of generic axiumbilics points. |
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