On Holomorphic Isometries into Blow-Ups of Cn.

We study the Kähler-Einstein manifolds which admits a holomorphic isometry into either the generalized Burns-Simanca manifold ( C ~ n , g S) or the Eguchi-Hanson manifold ( C ~ 2 , g EH) . Moreover, we prove that ( C ~ n , g S) and ( C ~ 2 , g EH) are not relatives to any homogeneous bounded domain. [ABSTRACT FROM AUTHOR]