ETDs @PUC-Rio
| Título: | REPRESENTATION OF GENERIC CURVES BY THEIR SINGULARITIES | ||||||||||||
| Autor: |
FILIPE BELLIO DA NOBREGA |
||||||||||||
| Colaborador(es): |
MARCOS CRAIZER - Orientador |
||||||||||||
| Catalogação: | 08/JAN/2019 | Língua(s): | ENGLISH - UNITED STATES |
||||||||||
| Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
| Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
||||||||||||
| Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=36011&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=36011&idi=2 |
||||||||||||
| DOI: | https://doi.org/10.17771/PUCRio.acad.36011 | ||||||||||||
| Resumo: | |||||||||||||
|
The aim of this work is to study the topological and geometric properties of closed generic immersed curves in the plane. In this case, generic means that the curve can only have double points without a common tangent. One can label the singularities using n symbols, such as a1, ... , an. Going around the curve, a cyclic word of length 2n is produced. However, not every word is related to a planar curve, there are requirements on its combinatorics, the first of which was found by Gauss. Advances were made in the study of locally convex curves on the plane, the sphere and the projective plane.
|
|||||||||||||
|
|||||||||||||