Algebraic & Geometric Topology

Engel structures with trivial characteristic foliations

Jiro Adachi

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882691

Digital Object Identifier
doi:10.2140/agt.2002.2.239

Mathematical Reviews number (MathSciNet)
MR1917051

Zentralblatt MATH identifier
1008.53061

Subjects
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.)

Keywords
Engel structure prolongation Legendrian foliation

Citation

Adachi, Jiro. Engel structures with trivial characteristic foliations. Algebr. Geom. Topol. 2 (2002), no. 1, 239--255. doi:10.2140/agt.2002.2.239. https://projecteuclid.org/euclid.agt/1513882691


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References

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