| Texto completo | |
| Autor(es): |
Dias, Fabio Scalco
;
Tari, Farid
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | TOHOKU MATHEMATICAL JOURNAL; v. 68, n. 2, p. 293-328, JUN 2016. |
| Citações Web of Science: | 1 |
| Resumo | |
We initiate in this paper the study of the geometry of the cross-cap in Minkowski 3-space R-1(3). We distinguish between three types of cross caps according to their tangential line being spacelike, timelike or lightlike. For each of these types, the principal plane which is generated by the tangential line and the limiting tangent direction to the curve of self-intersection of the cross-cap plays a key role. We obtain special parametrisations for the three types of cross-caps and consider their affine properties. The pseudo-metric on the cross-cap changes signature along a curve and the singularities of this curve depend on the type of the cross-cap. We also study the binary differential equations of the lightlike curves and of the principal curves in the parameters space and obtain their topological models as well as the configurations of their solution curves. (AU) | |
| Processo FAPESP: | 11/21240-4 - Teoria das singularidades e geometria de subvariedades no espaço Minkowski |
| Beneficiário: | Farid Tari |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 11/01946-0 - Um estudo sobre a geometria de curvas planas e superfícies em R4 |
| Beneficiário: | Fabio Scalco Dias |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 14/00304-2 - Singularidades de aplicações diferenciáveis: teoria e aplicações |
| Beneficiário: | Maria Aparecida Soares Ruas |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |