ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE

Autor(es)

Oset Sinha, Raul ^[1] ; Tari, Farid ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: OSAKA JOURNAL OF MATHEMATICS; v. 55, n. 3, p. 393-421, JUL 2018.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 14/00304-2 - Singularidades de aplicações diferenciáveis: teoria e aplicações
• Beneficiário: Maria Aparecida Soares Ruas
• Modalidade de apoio: Auxílio à Pesquisa - Temático