Tohoku Mathematical Journal

Contact pairs

Gianluca Bande and Amine Hadjar

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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.

Article information

Tohoku Math. J. (2), Volume 57, Number 2 (2005), 247-260.

First available in Project Euclid: 27 June 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D10: Contact manifolds, general
Secondary: 57R17: Symplectic and contact topology

Contact geometry Reeb vector field complementary foliations invariant forms


Bande, Gianluca; Hadjar, Amine. Contact pairs. Tohoku Math. J. (2) 57 (2005), no. 2, 247--260. doi:10.2748/tmj/1119888338.

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