Taut and Tight Complex Manifolds

Theodore J. Barth
1970 Proceedings of the American Mathematical Society  
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.
doi:10.2307/2037381 fatcat:cep2rldv3fab3pfbotox2uugyu