  We study the K\"ahler-Einstein manifolds which admits a holomorphic isometry
into either the generalized Burns-Simanca manifold $(\tilde {\mathbb C}^n,
g_S)$ or the Eguchi-Hanson manifold $(\tilde {\mathbb C}^2, g_{EH})$. Moreover,
we prove that $(\tilde {\mathbb C}^n, g_S)$ and $(\tilde {\mathbb C}^2,
g_{EH})$ are not relatives to any homogeneous bounded domain.
