Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T23:59:34.693Z Has data issue: false hasContentIssue false
  • English
  • Français

Topology of Some Kähler Manifolds II

Published online by Cambridge University Press:  20 November 2018

K. Srinivasacharyulu
K. Srinivasacharyulu*
Affiliation:
Universitedé Montreal
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.

Topology of positively curved compact Kähler manifolds had been studied by several authors (cf. [6; 2]); these manifolds are simply connected and their second Betti number is one [1]. We will restrict ourselves to the study of some compact homogeneous Kähler manifolds. The aim of this paper is to supplement some results in [9]. We prove, among other results, that a compact, simply connected homogeneous complex manifold whose Euler number is a prime p ≥ 2 is isomorphic to the complex projective space Pp-1 (C); in the p-1 case of surfaces, we prove that a compact, simply connected, homogeneous almost complex surface with Euler-Poincaré characteristic positive, is hermitian symmetric.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 457 - 460
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Bishop, R. L. and Goldberg, S. I., On the second cohomology group of a Kähler manifold of positive curvature. Proc. Amer. Math. Soc. 16 (1965) 119–122.Google Scholar
2. Bishop, R. L. and Goldberg, S.I., Some implications of the generalized Gauss-Bonnet theorem. Trans. Amer. Math. Soc. 112 (1964) 508–535.Google Scholar
3. Bishop, R. L. and Goldberg, S.I., Rigidity of positively curved Kahler manifolds. Proc. Nat. Acad. Sci., U.S.A. 54 (1965) 1037–1041.Google Scholar
4. Borel, A. and de Siebenthal, J., Les sous-groupes fermés de rang maximum des gróupes de Lie clos. Commentari Math. Helv. 23 (1949) 202–221.Google Scholar
5. Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces I. Amer. J. Math. 80 (1958) 458–538.Google Scholar
6. Frankel, T., Manifolds with positive curvature. Pac. J. Math. 11 (1961) 165–174.Google Scholar
7. Hermann, R., Compact homogeneous almost complex spaces of positive characteristic. Trans. Amer. Math. Society 83 (1956) 471–481.Google Scholar
8. Kobayashi, S., On compact Kähler manifolds with positive definite Ricci tensor. Ann. of Math. 74 (1961) 570–574.Google Scholar
9. Srinivasacharyulu, K., Topology of some Kähler manifolds, Pac. J. Math. 23 (1967) 167–169.Google Scholar
10. Srinivasacharyulu, K., On complex homogeneous manifolds. Can. Math. Bull. 10 (1967) 251–256.Google Scholar
11. Srinivasacharyulu, K., Topology of complex manifolds. Can. Math. Bull. 9 (1966) 23.Google Scholar