Flexibility for tangent and transverse immersions in Engel manifolds

Á. del Pino, F. Presas

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study the space of immersions of S1 that are tangent to an Engel structure D. We show that the full h-principle holds as soon as one excludes the closed orbits of W, the characteristic foliation of D. This is sharp: we elaborate on work of Bryant and Hsu to show that curves tangent to W sometimes form additional isolated components that cannot be detected at a formal level. We then show that this is an exceptional phenomenon: if D is C∞-generic, curves tangent to W are not isolated anymore. These results, in conjunction with an argument due to M. Gromov, prove that a full h-principle holds for immersions transverse to the Engel structure.
Original languageEnglish
Pages (from-to)215–238
JournalRevista Matematica Complutense
Volume32
DOIs
Publication statusPublished - 15 Jan 2019

Keywords

  • Engel structure
  • Horizontal curve
  • h-principle

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