Some results concerning hyperbolic manifolds
Author:
Peter Kiernan
Journal:
Proc. Amer. Math. Soc. 25 (1970), 588-592
MSC:
Primary 32.40; Secondary 53.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257393-9
MathSciNet review:
0257393
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Abstract | References | Similar Articles | Additional Information
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.
- Shoshichi Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460–480. MR 232411, DOI https://doi.org/10.2969/jmsj/01940460 ---, Hyperbolic manifolds and holomorphic mappings, Lecture Notes in Math., Springer, New York (to appear).
- Myung H. Kwack, Generalization of the big Picard theorem, Ann. of Math. (2) 90 (1969), 9–22. MR 243121, DOI https://doi.org/10.2307/1970678
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Keywords:
Hyperbolic,
Kobayashi pseudo-distance,
big Picard theorem,
fibre bundle,
completion,
locally compact
Article copyright:
© Copyright 1970
American Mathematical Society