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.
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