| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Valencia, Dept Geometria & Topol, C Dr Moliner 50, E-46100 Valencia - Spain
[2] Inst Ciencias Matemat & Comp USP, Ave Trabalhador Sao Carlense 400 Ctr, BR-13566590 Sao Carlos, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | OSAKA JOURNAL OF MATHEMATICS; v. 55, n. 3, p. 393-421, JUL 2018. |
| Web of Science Citations: | 3 |
| Abstract | |
We study the geometry of the cuspidal edge M in R-3 derived from its contact with planes and lines (referred to as flat geometry). The contact of M with planes is measured by the singularities of the height functions on M. We classify submersions on amodel of M by diffeomorphisms and recover the contact of M with planes from that classification. The contact of M with lines is measured by the singularities of orthogonal projections of M. We list the generic singularities of the projections and obtain the generic deformations of the apparent contour (profile) when the direction of projection varies locally in S-.(2) We also relate the singularities of the height functions and of the projections to some geometric invariants of the cuspidal edge. (AU) | |
| FAPESP's process: | 14/00304-2 - Singularities of differentiable mappings: theory and applications |
| Grantee: | Maria Aparecida Soares Ruas |
| Support Opportunities: | Research Projects - Thematic Grants |