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

Weiping Yin·Liyou Zhang
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Abstract

The explicit complete Einstein-Kähler 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-Kähler 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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Weiping Yin, Liyou Zhang. 2005-12-09. Complete Einstein-Kähler Metric and Holomorphic Sectional Curvature on $Y_{II}(r,p;K)$. https://arxiv.org/abs/math/0512183

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