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Classification of compact complex homogeneous spaces with invariant volumes
Author:
Daniel Guan
Journal:
Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 90-92
MSC (1991):
Primary 53C15, 57T15, 53C30, 53C56, 53C50
Posted:
August 29, 1997
MathSciNet review:
1465831
Full-text PDF Free Access
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Additional Information
Abstract: In this note we give a classification of compact complex homogeneous spaces with invariant volume.
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- [BR]
- A. Borel and R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann. 145 (1962), 429-439. MR 26:3088
- [DG1]
- J. Dorfmeister and Z. Guan, Classifications of compact homogeneous pseudo-Kähler manifolds, Comm. Math. Helv. 67 (1992), 499-513. MR 93i:32042
- [DG2]
- J. Dorfmeister and Z. Guan, Fine structure of reductive pseudo-Kählerian spaces, Geom. Dedi. 39 (1991), 321-338. MR 92h:53081
- [DG3]
- J. Dorfmeister and Z. Guan, Pseudo-Kählerian homogeneous spaces admitting a reductive transitive group of automorphisms, Math. Z. 209 (1992), 89-100. MR 92k:32058
- [DN]
- J. Dorfmeister and K. Nakajima, The fundamental conjecture for homogeneous Kähler manifolds, Acta. Math. 161 (1988), 23-70. MR 89i:32066
- [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. 63 (1996), 217-225. CMP 97:02
- [Gu3]
- D. Guan, Classification of compact complex homogeneous spaces with invariant volumes. Preprint.
- [Gu4]
- D. Guan, Classification of compact homogeneous spaces with invariant symplectic structures. Preprint.
- [Ha1]
- J. Hano, Equivariant projective immersion of a complex coset space with non-degenerate canonical Hermitian form, Scripta Math. 29 (1971), 125-139. MR 51:3557
- [Ha2]
- J. Hano, On compact complex coset spaces of reductive Lie groups, Proceedings of AMS 15 (1964), 159-163. MR 28:1258
- [Hk]
- A. T. Huckleberry, Homogeneous pseudo-Kählerian manifolds: A Hamiltonian viewpoint, Preprint, 1990.
- [HK]
- J. Hano and S. Kobayashi, A fibering of a class of homogeneous complex manifolds, Trans. Amer. Math. Soc. 94 (1960), 233-243. MR 22:5990
- [Kz]
- J. L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Canad. J. Math. 7 (1955), 562-576. MR 17:1109a
- [Mt1]
- Y. Matsushima, Sur les espaces homogènes kählériens d'un groupe de Lie réductif, Nagoya Math. J. 11 (1957), 53-60. MR 19:315c
- [Mt2]
- Y. Matsushima, Sur certaines variétés homogènes complexes, Nagoya Math. J. 18 (1961), 1-12. MR 25:2147
- [Ti]
- J. Tits, Espaces homogènes complexes compacts, Comm. Math. Helv. 37 (1962), 111-120. MR 27:4248
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- H. C. Wang, Complex parallisable manifolds, Proc. Amer. Math. Soc. 5 (1954), 771-776. MR 17:531a
- [Wa2]
- H. C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math. 79 (1954), 1-32. MR 16:518a
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Additional Information
Daniel Guan
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544
Email:
zguan@math.princeton.edu
DOI:
http://dx.doi.org/10.1090/S1079-6762-97-00028-0
PII:
S 1079-6762(97)00028-0
Keywords:
Invariant volume,
homogeneous,
product,
fiber bundles,
complex manifolds,
parallelizable manifolds,
discrete subgroups,
classifications
Received by editor(s):
May 30, 1997
Posted:
August 29, 1997
Additional Notes:
Supported by NSF Grant DMS-9401755 and DMS-9627434.
Communicated by:
Svetlana Katok
Article copyright:
© Copyright 1997 American Mathematical Society
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