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  "body": "\n## Summary\n\nAn Oka manifold is a complex manifold $Y$ that receives many holomorphic maps from Euclidean spaces.\nHolomorphic maps from neighbourhoods of compact convex sets in $\\C^n$ to $Y$ can be approximated by entire maps $\\C^n \\to Y$.\nFor such targets the Oka principle holds: every continuous map from a Stein manifold to $Y$ can be deformed to a holomorphic map.\nOka manifolds are the opposite of Kobayashi hyperbolic manifolds, which receive no nonconstant entire maps from $\\C$.\n\n## Explanations\n\n### L1 human\n\nSome complex manifolds are \"flexible\": they contain many holomorphic images of $\\C$ and of $\\C^n$, as $\\C^n$ itself does.\nOthers are \"rigid\": every holomorphic map from $\\C$ into them is constant, as for the unit disc, by Liouville's theorem.\nOka manifolds are the flexible ones, made precise by an approximation property.\nExamples are $\\C^n$, the complex projective spaces, and complex Lie groups such as $\\C^* = \\C \\setminus \\set{0}$.\n",
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