Engel structures with trivial characteristic foliations

Engel structures on $M \times S^{1}$ and $M \times I$ 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 $M \times \partial I$ in the case of $M \times I$ .

Keywords

Engel structure, prolongation, Legendrian foliation

Mathematical Subject Classification 2000

Primary: 57R25

Secondary: 58A17, 58A30, 53C15

References

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Publication

Received: 12 March 2002

Accepted: 22 March 2002

Published: 11 April 2002

Authors

Jiro Adachi
Department of Mathematics Osaka University Toyonaka Osaka 560-0043 Japan

Volume 2, issue 1 (2002)

Jiro Adachi