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Holomorphic fiber bundles with hyperbolic fiber


Author: H. L. Royden
Journal: Proc. Amer. Math. Soc. 43 (1974), 311-312
MSC: Primary 32L05; Secondary 32H20
DOI: https://doi.org/10.1090/S0002-9939-1974-0338465-0
MathSciNet review: 0338465
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Abstract: The purpose of the present note is to show that holomorphic fiber bundles with hyperbolic fiber are almost trivial: They are trivial if the base is simply connected, and have a simple structure otherwise.


References [Enhancements On Off] (What's this?)

  • [1] P. Kiernan, Results concerning hyperbolic manifolds, Proc. Amer. Math. Soc. 25 (1970), 588-592. MR 41 #2044. MR 0257393 (41:2044)
  • [2] S. Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460-480. MR 38 #736. MR 0232411 (38:736)
  • [3] -, Hyperbolic manifolds and holomorphic mappings, Pure and Appl. Math., vol. 2, Dekker, New York, 1970. MR 43 #3503. MR 0277770 (43:3503)
  • [4] H. L. Royden, Remarks on the Kobayashi metric, Proc. Maryland Conf. on Several Complex Variables, Lecture Notes in Math., vol. 185, Springer-Verlag, Berlin and New York. MR 0304694 (46:3826)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0338465-0
Keywords: Holomorphic fiber bundles, hyperbolic manifolds, Kobayashi, hyperbolicity, tight manifolds
Article copyright: © Copyright 1974 American Mathematical Society

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