Finite type ξ-asymptotic lines of plane fields in R^3

Douglas H. da Cruz and Ronaldo A. Garcia

Journal of Singularities
volume 22 (2020), 17-27

Received: 20 March 2019.

DOI: 10.5427/jsing.2020.22b

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Abstract:

We prove that a finite type curve is a ξ-asymptotic line (without parabolic points) of a suitable plane field. It is also given an explicit example of a hyperbolic closed finite type ξ-asymptotic line. These results obtained here are generalizations, for plane fields, of the results of V. Arnold.

Author(s) information:

Douglas H. da Cruz
Instituto de Matemática e Estatística
Universidade Federal de Goiás, Campus Samambaia
74690-900 - Goiânia -G0 - Brazil
email: douglashilariodacruz@gmail.com

Ronaldo A. Garcia
Instituto de Matemática e Estatística
Universidade Federal de Goiás, Campus Samambaia
74690-900 - Goiânia -G0 - Brazil
email: ragarcia@ufg.br