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## Canonical metrics on Cartan--Hartogs domains

### Abstract

In this paper we address two problems concerning a family of domains $M_{\Omega}(\mu) \subset \C^n$, called Cartan-Hartogs domains, endowed with a natural Kaehler metric $g(\mu)$. The first one is determining when the metric $g(\mu)$ is extremal (in the sense of Calabi), while the second one studies when the coefficient $a_2$ in the Engli\v{s} expansion of Rawnsley $\epsilon$-function associated to $g(\mu)$ is constant.Comment: 13 page

Topics: Mathematics - Differential Geometry, Mathematics - Complex Variables, 53C55, 32Q15, 32T15
Year: 2011
DOI identifier: 10.1142/S0219887812500119
OAI identifier: oai:arXiv.org:1104.5686