An example of a pseudoconvex domain whose holomorphic
sectional curvature of the
Bergman metric is unbounded
Annales Polonici Mathematici, Tome 92 (2007) no. 1, pp. 29-39
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
positive integers domain bbb holomorphic sectional curvature x bergman metric direction tends infty tends non tangentially direction suitably chosen seems example feature has known far
Affiliations des auteurs :
Gregor Herbort 1
@article{10_4064_ap92_1_3,
author = {Gregor Herbort},
title = {An example of a pseudoconvex domain whose holomorphic
sectional curvature of the
{Bergman} metric is unbounded},
journal = {Annales Polonici Mathematici},
pages = {29--39},
publisher = {mathdoc},
volume = {92},
number = {1},
year = {2007},
doi = {10.4064/ap92-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/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) no. 1, pp. 29-39. doi: 10.4064/ap92-1-3
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