Canonical metrics on Hartogs domains
Loi, Andrea ; Zuddas, Fabio
Osaka J. Math., Tome 47 (2010) no. 1, p. 507-521 / Harvested from Project Euclid
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An $n$-dimensional Hartogs domain $D_{F}$ can be equipped with a natural Kähler metric $g_{F}$. This paper contains two results. In the first one we prove that if $g_{F}$ is an extremal Kähler metric then $(D_{F}, g_{F})$ is holomorphically isometric to an open subset of the $n$-dimensional complex hyperbolic space. In the second one we prove the same assertion under the assumption that there exists a real holomorphic vector field $X$ on $D_{F}$ such that $(g_{F}, X)$ is a Kähler--Ricci soliton.
Publié le : 2010-06-15
Classification:  53C55,  32Q15,  32T15 
@article{1277298915,
     author = {Loi, Andrea and Zuddas, Fabio},
     title = {Canonical metrics on Hartogs domains},
     journal = {Osaka J. Math.},
     volume = {47},
     number = {1},
     year = {2010},
     pages = { 507-521},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1277298915}
}

Loi, Andrea; Zuddas, Fabio. Canonical metrics on Hartogs domains. Osaka J. Math., Tome 47 (2010) no. 1, pp.  507-521. http://gdmltest.u-ga.fr/item/1277298915/