Engel structures and weakly hyperbolic flows on four-manifolds

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

Abstract

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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0010-2571
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English