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Kotschick, Dieter; Vogel, Thomas (2018): Engel structures and weakly hyperbolic flows on four-manifolds. In: Commentarii Mathematici Helvetici, Vol. 93, No. 3: pp. 475-491


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.