Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-14T14:57:02.233Z Has data issue: false hasContentIssue false
  • English
  • Français

Topology of Complex Manifolds

Published online by Cambridge University Press:  20 November 2018

K. Srinivasacharyulu
K. Srinivasacharyulu*
Affiliation:
Université de Montréal and Summer Research Institute, Canadian Mathematical Congress
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.

The aim of this paper is to collect some interesting unsolved problems in the topology of compact complex manifolds which are scattered in literature; needless to remark, some of them are known to specialists. Besides, the readermay consult the well-known list of problems by F. Hirzebruch [ 5 ] which has stimulated remarkable progress in this direction. But the topology of complex manifolds has always baffled workers in this field and is still far from satisfactory. Of course, there is remarkable progress in the case of homogeneous compact complex manifolds. We start with the following result.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 1 , April 1966 , pp. 23 - 27
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bishop, R. L. and Goldberg, S.I., a) On curvature and Euler-Poincaré characteristic, Proc. Nat. Acad. Sci. U.S.A., Vol. 49 (1963), pp. 814-817. b) On the second cohomology group of a Kähler manifold of positive curvature, Proc. Amer. Math. Soc. Vol. 16, (1965), pp.119–122.Google Scholar
2. Calabi, E., Construction and properties of some 6-dimensionaI almost complex manifolds, Trans. Amer. Math. Soc. Vol. 87 (1958), pp. 407-438.Google Scholar
3. Ehresmann, C., Sur les variétés presque-complexes, Proc. of International Congress of Math. 1950, Vol. II (1952), pp. 412-419.Google Scholar
4. Hano, J., On Kählerian homogeneous spaces of unimodula: Lie groups, Amer. Jour. Math. Vol- 79 (1957), pp.885-900.Google Scholar
5. Hirzebruch, F., Some problems on differentiable and complex manifolds, Arm. of Math. Vol. 60(1954), pp. 213-236.Google Scholar
6. Igusa, I., On the structure of a certain class of Kähler varieties, Amer. Jour. Math. Vol. 76 (1954), pp.669-677.Google Scholar
7. Kodaira, K., On the structure of compact complex analytic surfaces I, Amer. Jour. Math. Vol. (1964), pp. 751-798.Google Scholar
8. Nagata, M., On rational surfaces I-II, Mem. Sci. Kyoto, Series A, Vol. 32(1959), pp. 352-370.Google Scholar
9. Serre, J. P., On the fundamental group of a Unirational variety, Jour. London Math. Soc. Vol. 34 (1959), pp. 481-484.Google Scholar
10. Srinivusacharyulu, K., On compact complex surfaces. To appear.Google Scholar