Curvature Properties of the Calabi-Yau Moduli

A curvature formula for the Weil-Petersson metric on the Calabi-Yau moduli spaces is given. Its relations to the Hodge metrics and the Bryant-Griffiths cubic form are obtained in the threefold case. Asymptotic behavior of the curvature near the boundary of moduli is also discussed via the theory of variations of Hodge structures.

2000 Mathematics Subject Classification: 32G20, 32Q25.

Keywords and Phrases: Weil-Petersson metric, Calabi-Yau manifold, variations of Hodge structures.

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