| Full text | |
| Author(s): |
Dias, Fabio Scalco
;
Tari, Farid
Total Authors: 2
|
| Document type: | Journal article |
| Source: | TOHOKU MATHEMATICAL JOURNAL; v. 68, n. 2, p. 293-328, JUN 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
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) | |
| FAPESP's process: | 11/21240-4 - Singularity theory and the geometry of submanifolds of the Minkowski space |
| Grantee: | Farid Tari |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 11/01946-0 - On the geometry of plane curves and surfaces in R4 |
| Grantee: | Fabio Scalco Dias |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 14/00304-2 - Singularities of differentiable mappings: theory and applications |
| Grantee: | Maria Aparecida Soares Ruas |
| Support Opportunities: | Research Projects - Thematic Grants |