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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some results concerning hyperbolic manifolds

Author: Peter Kiernan
Journal: Proc. Amer. Math. Soc. 25 (1970), 588-592
MSC: Primary 32.40; Secondary 53.00
MathSciNet review: 0257393
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Abstract: A complex manifold is (complete) hyperbolic if the Kobayashi pseudo-distance is a (complete) distance. In this note, it is shown that a fibre bundle is (complete) hyperbolic if both the base and fibre are (complete) hyperbolic. Two examples are also given. The first shows that the completion of a hyperbolic manifold is not necessarily locally compact. The second shows that one generalization of the big Picard theorem is false.

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

  • [1] Shoshichi Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460–480. MR 0232411
  • [2] -, Hyperbolic manifolds and holomorphic mappings, Lecture Notes in Math., Springer, New York (to appear).
  • [3] Myung H. Kwack, Generalization of the big Picard theorem, Ann. of Math. (2) 90 (1969), 9–22. MR 0243121

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Keywords: Hyperbolic, Kobayashi pseudo-distance, big Picard theorem, fibre bundle, completion, locally compact
Article copyright: © Copyright 1970 American Mathematical Society