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تسجيل مستخدم جديدOn normal contact pairs
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We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimotos Theorem on product of almost contact manifolds to flat bundles. We construct some examples on Boothby--Wang fibrations over contact-symplectic manifolds. In particular, these results give new methods to construct complex manifolds.
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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 $alphawedge dalpha^{k}wedgeeta
wedge deta^{h}$ 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.
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