#### Volume 2, issue 1 (2002)

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Engel structures with trivial characteristic foliations

Algebraic & Geometric Topology 2 (2002) 239–255
 arXiv: math.SG/0205100
##### Abstract

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

##### Keywords
Engel structure, prolongation, Legendrian foliation
##### Mathematical Subject Classification 2000
Primary: 57R25
Secondary: 58A17, 58A30, 53C15