On the Hodge Metric of the Universal Deformation Space of Calabi-Yau Threefolds

TL;DR

This paper explores the relationship between the Hodge metric and the Weil-Petersson metric on the moduli space of polarized Calabi-Yau threefolds, providing a new geometric understanding of their interplay.

Contribution

It expresses the Hodge metric explicitly in terms of the Weil-Petersson metric and its Ricci curvature, advancing the geometric analysis of Calabi-Yau moduli spaces.

Findings

Hodge metric expressed via Weil-Petersson metric

Relationship between Ricci curvature and Hodge metric clarified

Enhanced understanding of Calabi-Yau threefold moduli geometry

Abstract

In this paper, we represent the Hodge metric in terms of the Weil-Petersson metric and its Ricci curvature on the moduli spaces of polarized Calabi-Yau threefolds.