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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Engel structures with trivial characteristic foliations

Jiro Adachi

Algebraic & Geometric Topology 2 (2002) 239–255

arXiv: math.SG/0205100

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.

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