Hostname: page-component-669899f699-g7b4s Total loading time: 0 Render date: 2025-04-27T16:57:34.098Z Has data issue: false hasContentIssue false
  • English
  • Français

On Complex Homogeneous Manifolds

Published online by Cambridge University Press:  20 November 2018

K. Srinivasacharyulu
K. Srinivasacharyulu*
Affiliation:
Université de Montréal
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Compact complex homogeneous manifolds have been studied in great detail by Borel, Goto, Remmert and Wang (cf., (13)): it was shown that every compact, connected complex homogeneous manifold M is a holomorphic fiber bundle over a projective algebraic homogeneous manifold B with a connected, complex parallelizable fiber F.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 251 - 256
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Aeppli, A., Some Differential Geometric Remarks on Complex Homogeneous Manifolds. Arch. Math., 16 (1966) pages 60-68.Google Scholar
2. Borel, A., Kählerian Coset Spaces of Semi-simple Lie Groups. Proc. Nat. Acad. Sci. U. S. A. 40 (1955), pages 1147-1151.Google Scholar
3. Goldberg, S. I., Curvature and Homology. Academic Press (1966), page 225.Google Scholar
4. Goto, M., On Algebraic Homogeneous Spaces. Amer. J.Math. 76 (1955), pages 811-818.Google Scholar
5. Hirzebruch, F., Ubereine klasse von einfach - Zusammen - hangendenkomplexen Mannigfaltigkeiten. Math. Annalen, 124 (1955), pages 77-86.Google Scholar
6. Kodaira, K., (a) On Kähler Varieties of Restricted Type. Ann. of Math. 60 (1955), pages 28-48. (b) On Compact Complex Analytic Surfaces I. Ann. o. Math. 71 (1960), pages 111-152.Google Scholar
7. Kobayashi, S., On Compact Kähler Manifolds with Positive Definite Ricci Tensor. Ann. o. Math. 74 (1966), pages 570-576.Google Scholar
8. Koszul, J. L., Sur la forme hermitienne canonique des espaces homogènes complexes. Can. J.Math. 7 (1955), pages 562-576.Google Scholar
9. Lichenorowicz, A., Espaces homogènes Kähleriens. Colloque de Géomé. diffé., Strasbourg, C. N. R. S. (1955), pages 102-109.Google Scholar
10. Montgomery, D., Simply Connected Homogeneous Spaces. Proc. Amer. Math. Soc, 1 (1955), pages 467-469.Google Scholar
11. Nagata, M., On rational surfaces I - II. Mem. Sci. Kyoto, Sèrie. A, 32 (1955), pages 171-184.Google Scholar
12. Srinivasacharyulu, K., Topology of Complex Manifolds. Can. Math. Bulletin, 9 (1966), pages 23-27.Google Scholar
13. Wang, H. C., Some Geometrical Aspects of Coset Spaces of Lie Groups. Proc. International Cong, of Math., Camb. Univ. Press (1955), pages 500-509.Google Scholar