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Hyperbolic manifolds admitting holomorphic fiberings

Published online by Cambridge University Press:  17 April 2009

Subhashis Nag
Subhashis Nag
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India.
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Abstract

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We give a simple proof of the result that if the total space of a holomorphic fiber bundle is (complete) hyperbolic then both the fiber and the base manifold must be (complete) hyperbolic. Shoshichi Kobayashi tried to set up examples where the total space is hyperbolic but the base is not; our theorem shows that any such example is bound to fail.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 26 , Issue 2 , October 1982 , pp. 181 - 184
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Kiernan, Peter, “Some results concerning hyperbolic manifolds”, Proc. Amer. Math. Soc. 25 (1970), 588–592.CrossRefGoogle Scholar
[2]Kobayashi, Shoshichi, Hyperbolic manifolds and holomorphic mappings (Pure and Applied Mathematics, 2. Marcel Dekker, New York, 1970).Google Scholar
[3]Royden, H.L., “Holomorphic fiber bundles with hyperbolic fiber”, Proc. Amer. Math. Soc. 43 (1974), 311–312.CrossRefGoogle Scholar