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

Gregor Herbort

Gregor Herbort

Annales Polonici Mathematici, Tome 92 (2007), p. 29-39 / Harvested from The Polish Digital Mathematics Library

Résumé

Let a and m be positive integers such that 2a < m. We show that in the domain $D : = {z \in ℂ ³ | r (z) : = ℜ z ₁ + | z ₁ | ² + | z ₂ |}^{2 m} + {| z ₂ z ₃ |}^{2 a} + {| z ₃ |}^{2 m} < 0$ the holomorphic sectional curvature $R_{D} (z; X)$ of the Bergman metric at z in direction X tends to -∞ 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.

Publié le : 2007-01-01

Zbl 1133.32005

EUDML-ID : urn:eudml:doc:280308

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     author = {Gregor Herbort},
     title = {An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded},
     journal = {Annales Polonici Mathematici},
     volume = {92},
     year = {2007},
     pages = {29-39},
     zbl = {1133.32005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-3}
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Gregor Herbort. An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded. Annales Polonici Mathematici, Tome 92 (2007) pp. 29-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-3/