Algebraic and Geometric Topology 2 (2002), paper no. 11, pages 239-255.

Engel structures with trivial characteristic foliations

Jiro Adachi

Abstract. Engel structures on M x S^1 and M x 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, S^1 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 x dI in the case of M x I.

Keywords. Engel structure, prolongation, Legendrian foliation

AMS subject classification. Primary: 57R25. Secondary: 58A17, 58A30, 53C15.

DOI: 10.2140/agt.2002.2.239

E-print: arXiv:math.SG/0205100

Submitted: 12 March 2002. Accepted: 22 March 2002. Published: 11 April 2002.

Notes on file formats

Jiro Adachi
Department of Mathematics, Osaka University
Toyonaka Osaka 560-0043, Japan
and
Department of Mathematics, University of Pennsylvania
Philadelphia, PA 19104, USA
Email: adachi@math.sci.osaka-u.ac.jp, jiro@math.upenn.edu

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