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 $({\tilde{\mathbb{C}}}^n,g_S)$ 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.

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• Some remarks on homogeneous Kähler manifolds
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Cited by in corpus (3)

• Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds
• Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds
• On weak and strict relatives Kähler manifolds