#### 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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