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2005 Contact pairs
Gianluca Bande, Amine Hadjar
Tohoku Math. J. (2) 57(2): 247-260 (2005). DOI: 10.2748/tmj/1119888338

Abstract

We introduce a new geometric structure on differentiable manifolds. A Contact Pair on a $2h+2k+2$-dimensional manifold $M$ is a pair $(\alpha,\eta) $ of Pfaffian forms of constant classes $2k+1$ and $2h+1$, respectively, whose characteristic foliations are transverse and complementary and such that $\alpha$ and $\eta$ restrict to contact forms on the leaves of the characteristic foliations of $\eta$ and $\alpha$, respectively. Further differential objects are associated to Contact Pairs: two commuting Reeb vector fields, Legendrian curves on $M$ and two Lie brackets on the set of differentiable functions on $M$. We give a local model and several existence theorems on nilpotent Lie groups, nilmanifolds, bundles over the circle and principal torus bundles.

Citation

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Gianluca Bande. Amine Hadjar. "Contact pairs." Tohoku Math. J. (2) 57 (2) 247 - 260, 2005. https://doi.org/10.2748/tmj/1119888338

Information

Published: 2005
First available in Project Euclid: 27 June 2005

zbMATH: 1084.53064
MathSciNet: MR2137469
Digital Object Identifier: 10.2748/tmj/1119888338

Subjects:
Primary: 53D10
Secondary: 57R17

Rights: Copyright © 2005 Tohoku University

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