Homogeneous symplectic manifolds with Ricci-type curvature

Abstract

We consider invariant symplectic connections $\nabla$ on homogeneous symplectic manifolds $(M,\omega )$ with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an integrable almost complex structure on the bundle of almost complex structures compatible with the symplectic structure. If $M$ is compact with finite fundamental group then $(M,\omega )$ is symplectomorphic to $¶_n(\C)$ with a multiple of its Kähler form and $\nabla$ is affinely equivalent to the Levi-Civita connection.

Cited by in corpus (6)

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• Twistor theory of symplectic manifolds
• On invariants of almost symplectic connections
• Remarks on symplectic sectional curvature
• Curvature in Hamiltonian Mechanics And The Einstein-Maxwell-Dilaton Action
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