Oka manifold

Summary

An Oka manifold is a complex manifold $Y$ that receives many holomorphic maps from Euclidean spaces. Holomorphic maps from neighbourhoods of compact convex sets in $\C^n$ to $Y$ can be approximated by entire maps $\C^n \to Y$. For such targets the Oka principle holds: every continuous map from a Stein manifold to $Y$ can be deformed to a holomorphic map. Oka manifolds are the opposite of Kobayashi hyperbolic manifolds, which receive no nonconstant entire maps from $\C$.