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
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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.References
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
- H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193–233. MR 224869, DOI 10.1007/BF02392083
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