Balanced metrics on Cartan and Cartan-Hartogs domains

Abstract

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in [13] (Kaehler-Einstein submanifolds of the infinite dimensional projective space, to appear in Mathematische Annalen) we also provide the first example of complete, Kaehler-Einstein and projectively induced metric g such that $\alpha g$ is not balanced for all $\alpha >0$.

11 pages

References in corpus (2)

• Kaehler-Einstein submanifolds of the infinite dimensional projective space
• The Kaehler-Einstein metric for some Hartogs domains over bounded symmetric domains

Cited by in corpus (9)

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• Balanced metrics on some Hartogs type domains over bounded symmetric domains
• The Simanca metric admits a regular quantization
• Rawnsley's $\epsilon$-function on some Hartogs type domains over bounded symmetric domains and its applications
• Symplectic geometry of Cartan-Hartogs domains
• On the Szegö kernel of Cartan-Hartogs domains
• A Cartan-Hartogs version of the Polydisk Theorem