Engel structures and weakly hyperbolic flows on four-manifolds

  • D. Kotschick

    Universität München, Germany
  • Thomas Vogel

    Universität München, Germany


We study pairs of Engel structures on four-manifolds whose intersection has constant rank one and which define the same even contact structure, but induce different orientations on it. We establish a correspondence between such pairs of Engel structures and a class of weakly hyperbolic flows. This correspondence is analogous to the correspondence between bi-contact structures and projectively or conformally Anosov flows on three-manifolds found by Eliashberg–Thurston and by Mitsumatsu.

Cite this article

D. Kotschick, Thomas Vogel, Engel structures and weakly hyperbolic flows on four-manifolds. Comment. Math. Helv. 93 (2018), no. 3, pp. 475–491

DOI 10.4171/CMH/441