Tohoku Mathematical Journal 2005 June SECOND SERIES VOL. 57, NO. 2

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

Title CONTACT PAIRS

Author Gianluca Bande and Amine Hadjar

(Received August 11, 2003, revised June 18, 2004)
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.

2000 Mathematics Subject Classification. Primary 53D10; Secondary 57R17.

Key words and phrases. Contact geometry, Reeb vector field, complementary foliations, invariant forms.