Complete Einstein-Kähler Metric and Holomorphic Sectional Curvature on $Y_{II}(r,p;K)$

Details Complete Einstein-Kähler Metric and Holomorphic Sectional Curvature on $Y_{II}(r,p;K)$ Complete Einstein-Kähler Metric and Holomorphic Sectional Curvature on $Y_{II}(r,p;K)$

2005-12-09

arxiv.org/abs/math/0512183v1

Mathematics

Complex Variables

12 pages

Scientific paper

The explicit complete Einstein-K\"{a}hler metric on the second type Cartan-Hartogs domain $Y_{II}(r,p;K)$ is obtained in this paper when the parameter $K$ equals $\frac p2+\frac 1{p+1}$. The estimate of holomorphic sectional curvature under this metric is also given which intervenes between $-2K$ and $-\frac{2K}p$ and it is a sharp estimate. In the meantime we also prove that the complete Einstein-K\"ahler metric is equivalent to the Bergman metric on $Y_{II}(r,p;K)$ when $K=\frac p2+\frac 1{p+1}$.

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