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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Taut and tight complex manifolds
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by Theodore J. Barth
Proc. Amer. Math. Soc. 24 (1970), 429-431
DOI: https://doi.org/10.1090/S0002-9939-1970-0252679-6

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.
References
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • 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