Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T01:11:15.259Z Has data issue: false hasContentIssue false

First Chern class and holomorphic tensor fields

Published online by Cambridge University Press:  22 January 2016

Shoshichi Kobayashi*
Affiliation:
University of California, Berkeley
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.

Let M be an n-dimensional compact Kaehler manifold, TM its (holomorphic) tangent bundle and T*M its cotangent bundle. Given a complex vector bundle E over M, we denote its m-th symmetric tensor power by SmE and the space of holomorphic sections of E by Γ(E).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[1] Aubin, T., Equations du type Monge-Ampère sur le variétés kaehlériennes compactes, C. R. Acad. Sci. Paris 283 (1976), 119121.Google Scholar
[2] Berger, M., Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. math. France 83 (1955), 279330.Google Scholar
[3] Kobayashi, S., On compact Kaehler manifolds with positive definite Ricci tensor, Ann. Math. 74 (1961), 570574.CrossRefGoogle Scholar
[4] Kobayashi, S., The first Chern class and holomorphic symmetric tensor fields, to appear in J. Math. Soc. Japan 32-2 (1980).CrossRefGoogle Scholar
[5] Raynaud, M., Fibres vectoriels instables — Applications aux surfaces (d’après Bogomolov), Séminaire de Géométrie Algébrique, Orsay 1977/78, Exposé No. 3.Google Scholar
[6] Reid, M., Bogomolov’s theorem to appear.Google Scholar
[7] Yano, K. and Bochner, S., Curvature and Betti Numbers, Annals of Math. Studies No. 32, Princeton Univ. Press, 1953.CrossRefGoogle Scholar
[8] Yau, S. T., On the Ricci curvature of a compact Kaehler manifolds and the complex Monge-Ampère equations, I, Comm. Pure Appl. Math. 31 (1978), 339411.Google Scholar