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Proceedings of the American Mathematical Society

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

 
 

 

Taut and tight complex manifolds


Author: Theodore J. Barth
Journal: Proc. Amer. Math. Soc. 24 (1970), 429-431
MSC: Primary 32.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0252679-6
MathSciNet review: 0252679
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Abstract: Taut and tight manifolds, introduced recently by H. Wu, are characterized as follows. Let $ D$ denote the open unit disk in $ C$. The complex manifold $ N$ is taut iff the set $ A(D,N)$ of holomorphic maps from $ D$ into $ N$ is a normal family. If $ d$ is a metric inducing the topology on $ N,(N,d)$ is tight iff $ A(D,N)$ is equicontinuous. It is also shown that every taut manifold is tight in a suitable metric.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0252679-6
Keywords: Taut manifold, tight manifold, normal family, equicontinuous family
Article copyright: © Copyright 1970 American Mathematical Society

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