On the Geometry of Classifying Spaces and Horizontal Slices
| dc.creator | Lu, Zhiqin | |
| dc.date | 2005-05-26 | |
| dc.date.accessioned | 2026-07-07T05:20:18Z | |
| dc.date.available | 2026-07-07T05:20:18Z | |
| dc.description | In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let $U$ be a neighborhood of the moduli space. Then we know the universal covering space $V$ of $U$ is a smooth manifold. Suppose $D$ is the classifying space of a polarized Calabi-Yau manifold with the automorphism group $G$. Let $D_1$ be the symmetric space associated with $G$. Then we proved that the map from $V$ to $D_1$ induced by the period map is a pluriharmonic map. We also give a Kahler metric on $V$, which is called the Hodge metric. We proved that the Ricci curvature of the Hodge metric is negative away from zero. We also proved the non-existence of the Kähler metric on the classifying space of a Calabi-Yau threefold which is invariant under a cocompact lattice of $G$. | |
| dc.identifier | https://arxiv.org/abs/math/0505579 | |
| dc.identifier | http://arxiv.org/abs/math/0505579 | |
| dc.identifier | Amer. J. Math, vol 121, 1999, pp 177-198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75329 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 32G13, 58D27 | |
| dc.title | On the Geometry of Classifying Spaces and Horizontal Slices | |
| dc.type | text |