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The moment map for circle actions on symplectic manifolds. (English) Zbl 0696.53023
A theorem by T. Frankel [Ann. Math., II. Ser. 70, 1-8 (1959; Zbl 0088.380)] states that a complex symplectic circle action on a Kaehler manifold is Hamiltonian if and only if it has fixed points. This paper discusses possible generalizations to compact symplectic manifolds. The theorem is shown to hold in the case of four-dimensions but a counterexample in six dimensions is provided. Several interesting facts are presented in the discussion.
Reviewer: C.Günther

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
57S25 Groups acting on specific manifolds
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