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On the Integrability of Orthogonal Distributions in Poisson Manifolds

Dan Fish·Serge Preston
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Abstract

We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided.

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Dan Fish, Serge Preston. 2005-05-03. On the Integrability of Orthogonal Distributions in Poisson Manifolds. https://arxiv.org/abs/math/0405149

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