## Abstract

The asymptotic behavior of the holomorphic sectional curvature of the Bergman metric on a pseudoconvex Reinhardt domain of finite type in C^{2} is obtained by rescaling locally the domain to a model domain that is either a Thullen domain Ω_{m} = {(z_{1}, Z_{2}); [Z_{1}]^{2} + [Z_{2}]^{2m} < 1} or a tube domain T_{m} = {(z_{1}, Z_{2}); Imz_{1} + (Imz_{2})^{2m} < 1}. The Bergman metric for the tube domain T_{m} is explicitly calculated by using Fourier-Laplace transformation. It turns out that the holomorphic sectional curvature of the Bergman metric on the tube domain T_{m} at (0, 0) is bounded above by a negative constant. These results are used to construct a complete Kahler metric with holomorphic sectional curvature bounded above by a negative constant for a pseudoconvex Reinhardt domain of finite type in C^{2}.

Original language | English (US) |
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Pages (from-to) | 407-431 |

Number of pages | 25 |

Journal | Journal of Geometric Analysis |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - 1996 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Geometry and Topology

## Keywords

- Bergman metric
- Finite type
- Pseudoconvex
- Reinhardt domain
- Tube domain

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