Some results concerning hyperbolic manifolds
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- by Peter Kiernan
- Proc. Amer. Math. Soc. 25 (1970), 588-592
- DOI: https://doi.org/10.1090/S0002-9939-1970-0257393-9
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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
- Shoshichi Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460–480. MR 232411, DOI 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 10.2307/1970678
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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