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The Einstein-Kähler metrics on Cartan-Hartogs domain of the first type

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Abstract

Let Y I be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kähler metrics on Y I, the holomorphic sectional curvature of the invariant Einstein-Kähler metrics on Y I . The comparison theorem of complete Einstein-Kähler metric and Kobayashi metric on Y I is provided for some cases. For the non-homogeneous domain Y I, when \(K = \frac{{mn + 1}}{{m + n}},m > 1\), the explicit forms of the complete Einstein-Kähler metrics are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Capital Normal University, 100037, Beijing, China

    Wang An

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  1. Wang An
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Correspondence to Wang An.

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Wang, A. The Einstein-Kähler metrics on Cartan-Hartogs domain of the first type. Sci. China Ser. A-Math. 47, 220–235 (2004). https://doi.org/10.1360/02ys0043

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  • DOI: https://doi.org/10.1360/02ys0043

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