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<p>In this paper, we construct unbounded domains in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb C}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to 2, and that their holomorphic automorphism groups consist only of linear mappings.</p>

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Unbounded Reinhardt domains with finite-dimensional Bergman spaces in \({\mathbb C}^n\)

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Chika Hayashida,
  • Joe Kamimoto

摘要

In this paper, we construct unbounded domains in \({\mathbb C}^n\) C n ( \(n\ge 2\) n ≥ 2 ), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to 2, and that their holomorphic automorphism groups consist only of linear mappings.