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HOME > Table of Contents and Abstracts > Vol. 57, No. 2
Tohoku Mathematical Journal
2005
June
SECOND SERIES VOL. 57, NO. 2
Tohoku Math. J.
57 (2005), 247-260
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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.
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