We introduce a new geometric structure on differentiable manifolds. A Con- tact Pair on a 2h+2k+2-dimensional manifold M is a pair (α, η) of Pfaffian forms of constant classes 2k + 1 and 2h + 1, respectively, whose characteristic foliations are transverse and com- plementary and such that α and η restrict to contact forms on the leaves of the characteristic foliations of η and α, 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.
Contact Pairs
BANDE, GIANLUCA;
2005-01-01
Abstract
We introduce a new geometric structure on differentiable manifolds. A Con- tact Pair on a 2h+2k+2-dimensional manifold M is a pair (α, η) of Pfaffian forms of constant classes 2k + 1 and 2h + 1, respectively, whose characteristic foliations are transverse and com- plementary and such that α and η restrict to contact forms on the leaves of the characteristic foliations of η and α, 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.
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