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Negative Vector Bundles and Complex Finsler Structures

Published online by Cambridge University Press:  22 January 2016

Shoshichi Kobayashi
Shoshichi Kobayashi*
Affiliation:
University of California, Berkeley
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A complex Finsler structure F on a complex manifold M is a function on the tangent bundle T(M) with the following properties. (We denote a point of T(M) symbolically by (z, ζ), where z represents the base coordinate and ζ the fibre coordinate.)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 57 , June 1975 , pp. 153 - 166
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Goldberg, S. I. and Kobayashi, S., On holomorphic bisectional curvature, J. Differential Geometry 1 (1967), 225–233.CrossRefGoogle Scholar
[2] Grauert, H., Über Modifikationen und exzeptionelle analytische Mengen, Math. Annalen 146 (1962), 331–368.Google Scholar
[3] Griffiths, P. A., Hermitian differential geometry, Chern classes and positive vector bundles, Global Analysis in honor of Kodaira, 1969, 185–252.Google Scholar
[4] Hartshorne, R., Ample vector bundles, Publ. I. H. E. S. 29 (1966), 319–350.Google Scholar
[5] Kobayashi, S., Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, Inc. New York, 1970.Google Scholar
[6] Kobayashi, S. and Ochiai, T. On complex manifolds with positive tangent bundles, J. Math. Soc. Japan 22 (1970), 499–525.CrossRefGoogle Scholar
[7] Kobayashi, S. and Wu, H., On holomorphic sections of certain hermitian vector bundles, Math. Annalen 189 (1970), 1–4.Google Scholar
[8] Rizza, G. B., F-forme quadratiche ed hermitiane, Rend. Mat. e Appl. 23 (1965), 221–249.Google Scholar
[9] Rund, H., Generalized metrics on complex manifolds, Math. Nachrichten 34 (1967), 55–77.Google Scholar
[10] Rund, H., The Differential Geometry of Finsler Spaces, Springer-Verlag, 1959.CrossRefGoogle Scholar
[11] Schaeffer, H. H., Linear Topological Spaces, Macmillan, 1966.Google Scholar