English

Finite type $\xi$-asymptotic lines of plane fields in $\mathbb{R}^3$

Differential Geometry 2019-08-12 v1 Dynamical Systems

Abstract

We prove that a finite type curve is an ξ\xi-asymptotic line (without parabolic points) of a suitable plane field. It is also given an explicit example of a hyperbolic closed finite type ξ\xi-asymptotic line. These results obtained here are generalizations, for plane fields, of the results of V. Arnold [4].

Keywords

Cite

@article{arxiv.1908.03253,
  title  = {Finite type $\xi$-asymptotic lines of plane fields in $\mathbb{R}^3$},
  author = {Douglas H. da Cruz and Ronaldo A. Garcia},
  journal= {arXiv preprint arXiv:1908.03253},
  year   = {2019}
}

Comments

13 pages, 4 figures

R2 v1 2026-06-23T10:43:21.824Z