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- W1566009832 abstract "We introduce a new geometric structure on differentiable manifolds. A contact-symplectic pair on a manifold $M$ is a pair $left ( alpha ,eta right )$ where $alpha$ is a Pfaffian form of constant class $2k+1$ and $eta$ a $2$-form of constant class$ 2h$ such that $alpha wedge dalpha ^{k}wedge eta ^{h}$ is a volume form. Each form has a characteristic foliation whose leaves are symplectic and contact manifolds respectively. These foliations are transverse and complementary. Some other differential objects are associated to it. We give a local model and several existence theorems on nilpotent Lie groups, nilmanifolds and principal torus bundles. As a deep application of this theory, we give a negative answer to the famous Reebâs problem which asks if every vector field without closed 1-codimensional transversal on a manifold having contact forms is the Reeb vector field of a contact form." @default.
- W1566009832 created "2016-06-24" @default.
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- W1566009832 date "2002-11-20" @default.
- W1566009832 modified "2023-09-26" @default.
- W1566009832 title "Couples contacto-symplectiques" @default.
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- W1566009832 doi "https://doi.org/10.1090/s0002-9947-02-03209-9" @default.
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