Weil-Petersson geometry on moduli space of polarized Calabi-Yau manifolds
Differential Geometry
2007-05-23 v1 High Energy Physics - Theory
Abstract
In this paper, we define and study the Weil-Petersson geometry. Under the framework of the Weil-Petersson geometry, we study the Weil-Petersson metric and the Hodge metric. Among the other results, we represent the Hodge metric in terms of the Weil-Petersson metric and the Ricci curvature of the Weil-Petersson metric for Calabi-Yau fourfold moduli. We also prove that the Hodge volume of the moduli space is finite. Finally, we proved that the curvature of the Hodge metric is bounded if the Hodge metric is complete and the dimension of the moduli space is 1.
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Cite
@article{arxiv.math/0510020,
title = {Weil-Petersson geometry on moduli space of polarized Calabi-Yau manifolds},
author = {Zhiqin Lu and Xiaofeng Sun},
journal= {arXiv preprint arXiv:math/0510020},
year = {2007}
}
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