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Symplectic \(SO(3)\)-manifolds and their classification in dimension 4. (Les \(SO(3)\)-variétés symplectiques et leur classification en dimension 4.) (French) Zbl 0745.53027

It is shown that the principal stabilizer of any effective symplectic \(SO(3)\)-action on a symplectic manifold \(V\) is \(SO(2)\) or \(\mathbb{Z}/m\mathbb{Z}\). In the first case \(V\) is isomorphic to \(S^ 2\times V/SO(3)\). A complete classification is given of four-dimensional \(SO(3)\)-symplectic manifolds, both compact and non-compact.
Reviewer: F.Kirwan (Oxford)

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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References:

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