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| Canonical Metrics on Generalized Cartan-Hartogs Domains |
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Citation： |
Y. H. Hao.Canonical Metrics on Generalized Cartan-Hartogs Domains[J].Chinese Annals of Mathematics B,2016,37(3):357~366 |
| Page view： 1394
Net amount： 966 |
Authors： |
Y. H. Hao; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11371257) |
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| Abstract： |
In this paper, the author considers a class of bounded pseudoconvex
domains, i.e., the generalized Cartan-Hartogs domains
$\Omega(\mu,m)$. The first result is that the natural K\"ahler
metric $g^{\Omega(\mu,m)}$ of $\Omega(\mu,m)$ is extremal if and
only if its scalar curvature is a constant. The second result is
that the Bergman metric, the K\"ahler-Einstein metric, the
Carath\'eodary metric, and the Koboyashi metric are equivalent for
$\Omega(\mu,m)$. |
Keywords： |
Canonical metric, Extremal metric, Comparison theorem, Generalized
Cartan-Hartogs domains |
Classification： |
32A07, 32F45, 32Q15 |
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