Mathematics – Differential Geometry
Scientific paper
2003-05-27
Tohoku Math. J. 57 (2005), no. 2, 247--260
Mathematics
Differential Geometry
15 pages
Scientific paper
We introduce a new geometric structure on differentiable manifolds. A \textit{Contact} \textit{Pair}on a manifold $M$ is a pair $(\alpha,\eta) $ of Pfaffian forms of constant classes $2k+1$ and $2h+1$ respectively such that $\alpha\wedge d\alpha^{k}\wedge\eta\wedge d\eta^{h}$ is a volume form. Both forms have a characteristic foliation whose leaves are contact manifolds. These foliations are transverse and complementary. Further differential objects are associated to Contact Pairs: two commuting Reeb vector fields, Legendrian curves on $M$ and two Lie brackets on $\mathcal{C}^{\infty}(M) $. We give a local model and several existence theorems on nilpotent Lie groups, nilmanifolds, bundles over the circle and principal torus bundles.
Bande Gianluca
Hadjar Amine
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