Algebraic & Geometric Topology

Engel structures with trivial characteristic foliations

Jiro Adachi

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Engel structures on M×S1 and M×I are studied in this paper, where M is a 3–dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S1 or I. It is proved that they are characterized by contact structures on the cross section M, the twisting numbers, and Legendrian foliations on both ends M×I in the case of M×I.

Article information

Algebr. Geom. Topol., Volume 2, Number 1 (2002), 239-255.

Received: 12 March 2002
Accepted: 22 March 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R25: Vector fields, frame fields
Secondary: 58A17: Pfaffian systems 58A30: Vector distributions (subbundles of the tangent bundles) 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Engel structure prolongation Legendrian foliation


Adachi, Jiro. Engel structures with trivial characteristic foliations. Algebr. Geom. Topol. 2 (2002), no. 1, 239--255. doi:10.2140/agt.2002.2.239.

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