Wojciech Domitrz (2008)
Banach Center Publications
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We define a procedure of reduction of locally conformal symplectic structures. We find a necessary and sufficient condition for this reduction to hold in terms of a special kind of de Rham cohomology class (tangent to the characteristic foliation) of the Lee form.
Haller, Stefan, Rybicki, Tomasz
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Summary: It is proven that the Poisson algebra of a locally conformal symplectic manifold is integrable by making use of a convenient setting in global analysis. It is also observed that, contrary to the symplectic case, a unified approach to the compact and non-compact case is possible.
Dusa McDuff (1987)
Annales de l'institut Fourier
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We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures
León, Manuel de (1989)
Portugaliae mathematica
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Chinea, Domingo, de León, Manuel, Marrero, Juan C. (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Izu Vaisman (1990)
Annales de l'institut Fourier
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The paper begins with some general remarks which include the Mayer-Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochshild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic,...