Compatibility between pseudo-Riemannian structures and Poisson structures (Q2765892)
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scientific article; zbMATH DE number 1695103
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compatibility between pseudo-Riemannian structures and Poisson structures |
scientific article; zbMATH DE number 1695103 |
Statements
1 August 2002
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pseudo-Riemannian structure
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Poisson structure
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Compatibility between pseudo-Riemannian structures and Poisson structures (English)
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The author introduces two notions of compatibility between pseudo-Riemannian metrics and Poisson structures on a manifold \(M\).NEWLINENEWLINENEWLINEThe difficulty for finding such a condition is the fact that pseudo-Riemannian structures and Poisson structures are very different concepts, the first is covariant, the second is contravariant. In this paper, the author exploits the contravariant aspect. Using the notion of contravariant connections of \textit{R. L. Fernandes} [J. Differ. Geom. 54, No. 2, 303-365 (2000; Zbl 1036.53060)], the author presents two different notions of compatibility. Finally, the properties of such compatible structures are studied and examples are given.
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