An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded

Tom 92 / 2007

Gregor Herbort Annales Polonici Mathematici 92 (2007), 29-39 MSC: 32F45, 32T25. DOI: 10.4064/ap92-1-3

Streszczenie

Let $a$ and $m$ be positive integers such that $2a< m$. We show that in the domain $D:=\{ z\in \Bbb C^3\,|\, r(z):= \Re z_1 + |z_1|^2 + |z_2|^{2m} + |z_2z_3|^{2a}+|z_3|^{2m} <0\}$ the holomorphic sectional curvature $R_D(z;X)$ of the Bergman metric at $z$ in direction $X$ tends to $-\infty$ when $z$ tends to $0$ non-tangentially, and the direction $X$ is suitably chosen. It seems that an example with this feature has not been known so far.

Autorzy

  • Gregor HerbortBergische Universität Wuppertal
    Fachbereich C – Mathematik und Naturwissenschaften
    Gaußstraße 20
    D-42097 Wuppertal, German
    e-mail

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