Abstract
Let (Mn, w) be a Poisson manifold. According to the definition, as given at the beginning of Chapter 1, we expect the set \({{X}_{w}}(M)\mathop{ = }\limits^{{def}} \left. {\{ {{X}_{f}}\mid f \in {{C}^{\infty }}(M)} \right\}\) of the Hamiltonian vector fields of M to play an important role. In order to discover it, let us define
. Notice that, since Xf = #(df), where # is the homomorphism (1.3), we have Sx0(M) = im#x0. In order to speak of the set S(M) of all these planes, we shall adopt the following terminology, which is slightly different from that of the textbooks on differentiable manifolds.
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© 1994 Springer Basel AG
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Vaisman, I. (1994). The Symplectic Foliation of a Poisson Manifold. In: Lectures on the Geometry of Poisson Manifolds. Progress in Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8495-2_3
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DOI: https://doi.org/10.1007/978-3-0348-8495-2_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9649-8
Online ISBN: 978-3-0348-8495-2
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