Riemannian geometry of Hartogs domains
| dc.creator | Di Scala, Antonio J. | |
| dc.creator | Loi, Andrea | |
| dc.creator | Zuddas, Fabio | |
| dc.date | 2008-03-25 | |
| dc.date.accessioned | 2026-07-07T09:28:17Z | |
| dc.date.available | 2026-07-07T09:28:17Z | |
| dc.description | Let $D_F = \{(z_0, z) \in {\C}^{n} | |z_0|^2 < b, \|z\|^2 < F(|z_0|^2) \}$ be a strongly pseudoconvex Hartogs domain endowed with the \K metric $g_F$ associated to the \K form $ω_F = -\frac{i}{2} \partial \bar{\partial} \log (F(|z_0|^2) - \|z\|^2)$. This paper contains several results on the Riemannian geometry of these domains. In the first one we prove that if $D_F$ admits a non special geodesic (see definition below) through the origin whose trace is a straight line then $D_F$ is holomorphically isometric to an open subset of the complex hyperbolic space. In the second theorem we prove that all the geodesics through the origin of $D_F$ do not self-intersect, we find necessary and sufficient conditions on $F$ for $D_F$ to be geodesically complete and we prove that $D_F$ is locally irreducible as a Riemannian manifold. Finally, we compare the Bergman metric $g_B$ and the metric $g_F$ in a bounded Hartogs domain and we prove that if $g_B$ is a multiple of $g_F$, namely $g_B=λg_F$, for some $λ\in \R^+$, then $D_F$ is holomorphically isometric to an open subset of the complex hyperbolic space. | |
| dc.description | to appear in International Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/0803.3533 | |
| dc.identifier | http://arxiv.org/abs/0803.3533 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157400 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C55, 32Q15, 32T15 | |
| dc.title | Riemannian geometry of Hartogs domains | |
| dc.type | text |