Kotschick, D.; Vogel, T. Engel structures and weakly hyperbolic flows on four-manifolds. (English) Zbl 1402.37045 Comment. Math. Helv. 93, No. 3, 475-491 (2018). An {Engel structure} on a \(4\)-dimensional manifold \(M\) is a smooth rank-\(2\) distribution \(\mathcal{D}\) with the property that \([\mathcal{D}\),\( \mathcal{D]}\) is an even contact structure \(\mathcal{E}\) (i.e., a maximally non-integrable smooth hyperplane field \(\mathcal{E}\)).A { bi-Engel structure} on a \(4\)-dimensional manifold \(M\) is a pair of Engel structures \((\mathcal{D}_{+}\),\(\mathcal{D}_{-}\mathcal{)}\) inducing the same even contact structure \(\mathcal{E}\), defining opposite orientations for \(\mathcal{E}\) and having a one-dimensional intersection.In the paper under review, the authors study bi-Engel structures. The main result of the paper gives the correspondence between bi-Engel structures and a class of weakly hyperbolic flows. Reviewer: Andreea Olteanu (Bucureşti) Cited in 1 Document MSC: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 58A30 Vector distributions (subbundles of the tangent bundles) 37D30 Partially hyperbolic systems and dominated splittings 53D35 Global theory of symplectic and contact manifolds 53D10 Contact manifolds (general theory) Keywords:Engel structure; bi-Engel structure; hyperbolic flow; even contact structure PDFBibTeX XMLCite \textit{D. Kotschick} and \textit{T. Vogel}, Comment. Math. Helv. 93, No. 3, 475--491 (2018; Zbl 1402.37045) Full Text: DOI arXiv