Taut and tight complex manifolds

Taut and tight manifolds, introduced recently by H. Wu, are characterized as follows. Let D D denote the open unit disk in C C . The complex manifold N N is taut iff the set A ( D , N ) A(D,N) of holomorphic maps from D D into N N is a normal family. If d d is a metric inducing the topology on N , ( N , d ) N,(N,d) is tight iff A ( D , N ) A(D,N) is equicontinuous. It is also shown that every taut manifold is tight in a suitable metric.