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

Gregor Herbort. "An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded." Annales Polonici Mathematici 92.1 (2007): 29-39. <http://eudml.org/doc/280308>.

@article{GregorHerbort2007,
abstract = {Let a and m be positive integers such that 2a < m. We show that in the domain $D:= \{z ∈ ℂ³ | r(z):= ℜ z₁ + |z₁|² + |z₂|^\{2m\} + |z₂z₃|^\{2a\} + |z₃|^\{2m\} <0\}$ 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.},
author = {Gregor Herbort},
journal = {Annales Polonici Mathematici},
keywords = {Bergman metric; holomorphic sectional curvature},
language = {eng},
number = {1},
pages = {29-39},
title = {An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded},
url = {http://eudml.org/doc/280308},
volume = {92},
year = {2007},
}

TY - JOUR
AU - Gregor Herbort
TI - An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded
JO - Annales Polonici Mathematici
PY - 2007
VL - 92
IS - 1
SP - 29
EP - 39
AB - Let a and m be positive integers such that 2a < m. We show that in the domain $D:= {z ∈ ℂ³ | r(z):= ℜ z₁ + |z₁|² + |z₂|^{2m} + |z₂z₃|^{2a} + |z₃|^{2m} <0}$ 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.
LA - eng
KW - Bergman metric; holomorphic sectional curvature
UR - http://eudml.org/doc/280308
ER -