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Classification of compact homogeneous spaces with invariant symplectic structures
Author(s):
Daniel
Guan
Journal:
Electron. Res. Announc. Amer. Math. Soc.
3
(1997),
52-54.
MSC (1991):
Primary 53C15, 57S25, 53C30;
Secondary 22E99, 15A75
Posted:
July 29, 1997
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Abstract:
We solve a longstanding problem of classification of compact homogeneous spaces with invariant symplectic structures. We also give a splitting conjecture on compact homogeneous spaces with symplectic structures (which are not necessarily invariant under the group action) that makes the classification of this kind of manifolds possible.
References:
- [Bo]
- F. A. Bogomolov, On Guan's examples of simply connected non-Kähler compact complex manifolds, Amer. J. Math. 118 (1996), 1037-1046. CMP 97:01
- [BR]
- A. Borel and R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann. 145 (1962), 429-439. MR 26:3088
- [DG]
- J. Dorfmeister and Z. Guan, Classifications of compact homogeneous pseudo-Kähler manifolds, Comm. Math. Helv. 67 (1992), 499-513. MR 93i:32042
- [Gu1]
- Z. Guan, Examples of compact holomorphic symplectic manifolds which admit no Kähler structure. In Geometry and Analysis on Complex Manifolds-Festschrift for Professor S. Kobayashi's 60th Birthday, World Scientific, 1994, pp. 63-74.
- [Gu2]
- D. Guan, A splitting theorem for compact complex homogeneous spaces with a symplectic structure, Geom. Dedi. 67 (1996), 217-225. CMP 97:02
- [Gu3]
- D. Guan, Classification of compact complex homogeneous spaces with invariant volumes, preprint 1996.
- [Gu4]
- D. Guan, Examples of compact holomorphic symplectic manifolds which are not Kählerian II, Invent. Math. 121 (1995), 135-145. CMP 95:16
- [Hk]
- A. T. Huckleberry, Homogeneous pseudo-Kählerian manifolds: a Hamiltonian viewpoint, preprint, 1990.
- [Kb]
- S. Kobayashi, Differential geometry of complex vector bundles, Iwanami Shoten Publishers and Princeton University Press, 1987. MR 89e:53100
- [Mt]
- Y. Matsushima, Sur les espaces homogènes kählériens d`un groupe de Lie réductif, Nagoya Math. J. 11 (1957), 53-60. MR 19:315c
- [Ti]
- J. Tits, Espaces homogènes complexes compacts, Comm. Math. Helv. 37(1962), 111-120. MR 27:4248
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Additional Information:
Daniel
Guan
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544
Email:
zguan@math.princeton.edu
DOI:
10.1090/S1079-6762-97-00023-1
PII:
S 1079-6762(97)00023-1
Keywords:
Invariant structure,
homogeneous space,
product,
fiber bundles,
symplectic manifolds,
splittings,
prealgebraic group,
decompositions,
modification,
Lie group,
symplectic algebra,
compact manifolds,
uniform discrete subgroups,
classifications,
locally flat parallelizable manifolds
Received by editor(s):
February 21, 1997
Posted:
July 29, 1997
Additional Notes:
Supported by NSF Grant DMS-9401755 and DMS-9627434.
Communicated by:
Gregory Margulis
Copyright of article:
Copyright
1997,
American Mathematical Society
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