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On compact homogeneous symplectic manifolds

P. B. Zwart; William M. Boothby — 1980

Annales de l'institut Fourier

In this paper the authors study compact homogeneous spaces $G / K$ (of a Lie group $G$ ) on which there if defined a $G$ -invariant symplectic form $Ω$ . It is an important feature of the paper that very little is assumed concerning $G$ and $K$ . The essential assumptions are: (1) $G$ is connected and (2) $K$ is uniform (i.e., $G / K$ is compact). Further, for convenience only and with no loss of generality, it is supposed that $G$ is simply connected and $K$ contains no connected normal subgroup of $G$ , i.e., that $G$ acts almost effectively...

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