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Taut and tight complex manifolds

Author: Theodore J. Barth
Journal: Proc. Amer. Math. Soc. 24 (1970), 429-431
MSC: Primary 32.40
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.

References [Enhancements On Off] (What's this?)

  • [1] J. L. Kelley, General topology, Van Nostrand, Princeton, N. J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [2] S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. I, Interscience, New York, 1963. MR 27 #2945. MR 0152974 (27:2945)
  • [3] H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193-233. MR 37 #468. MR 0224869 (37:468)

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Keywords: Taut manifold, tight manifold, normal family, equicontinuous family
Article copyright: © Copyright 1970 American Mathematical Society

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