On holomorphic isometries into blow-ups of $\mathbb C^n$

Abstract

We study the Kähler-Einstein manifolds which admits a holomorphic isometry into either the generalized Burns-Simanca manifold ( Cn , g S ) or the Eguchi-Hanson manifold ( C2 , g EH ). Moreover, we prove that ( Cn , g S ) and( C2 , g EH ) are not relatives to any homogeneous bounded domain.

Holomorphic isometries into homogeneous bounded domains

“…If two such holomorphic isometries exist, (S, g S ) and (S ′ , g S ′ ) are said to be relatives ( [22] and [6]). For update results on relatives Kähler manifolds the reader is referred the survey paper [23] (see also the recent preprint [11]). Recently the authors of this paper extend the result in [4] for bounded symmetric domains to arbirtary homogeneous domain, by proving the following:…”