Frame and direction mappings for surfaces in R-3

Autor(es)

Bruce, J. W. ^[1] ; Tari, F. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Liverpool, Dept Math Sci, Math Sci Bldg, Liverpool L69 7ZL, Merseyside - England

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Ave Trabalhador Saocarlense, 400 Ctr, BR-13566590 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS; v. 149, n. 3, p. 795-830, JUN 2019.
• Citações Web of Science: 0

Resumo

We study frames in R-3 and mapping from a surface M in R-3 to the space of frames. We consider in detail mapping frames determined by a unit tangent principal or asymptotic direction field U and the normal field N. We obtain their generic local singularities as well as the generic singularities of the direction field itself. We show, for instance, that the cross-cap singularities of the principal frame map occur precisely at the intersection points of the parabolic and subparabilic curves of different colours. We study the images of the asymptotic and principal foliations on the unit sphere by their associated unit direction fields. We show that these curves are solutions of certain first order differential equations and point out a duality in the unit sphere between some of their configurations. (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