Title:
On Exact Poisson Structures

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Yi, Yingfei
Zhang, Xiang
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Abstract
By studying the exactness of multi-linear vectors on an orientable smooth manifold M, we give some characterizations to exact Poisson structures defi ned on M and study general properties of these structures. Following recent works [12, 13, 15], we will pay particular attention to the classification of some special classes of exact Poisson structures such as Jacobian and quasihomogeneous Poisson structures. A characterization of exact Poisson structures which are invariant under the flow of a class of completely integrable systems will also be given.
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The rst author was partially supported by NSF grant DMS0204119. The second author is partially supported by NSFC grant 10231020 and Shuguang plan of Shanghai.
Date Issued
2004
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