On compact symplectic manifolds with Lie group symmetries
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Abstract:
In this note we give a structure theorem for a finite-dimensional subgroup of the automorphism group of a compact symplectic manifold. An application of this result is a simpler and more transparent proof of the classification of compact homogeneous spaces with invariant symplectic structures. We also give another proof of the classification from the general theory of compact homogeneous spaces which leads us to a splitting conjecture on compact homogeneous spaces with symplectic structures (which are not necessary invariant under the group action) that makes the classification of this kind of manifold possible.References
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Additional Information
- Daniel Guan
- Affiliation: Department of Mathematics, University of California–Riverside, Riverside, California 92521
- Email: zguan@math.ucr.edu
- Received by editor(s): May 22, 2002
- Received by editor(s) in revised form: February 26, 2004
- Published electronically: March 10, 2005
- Additional Notes: This work was supported by NSF Grant DMS-9627434 and DMS-0103282
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 3359-3373
- MSC (2000): Primary 53C15, 57S25, 53C30, 22E99, 15A75
- DOI: https://doi.org/10.1090/S0002-9947-05-03657-3
- MathSciNet review: 2135752