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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.


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