Quasi-isometry and deformations of Calabi-Yau manifolds

Abstract

We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of Kähler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds and also a construction of global canonical family of holomorphic $(n,0)$-forms on the deformation spaces of Calabi-Yau manifolds. Similar constructions are also applied to the deformation spaces of compact Kähler manifolds.

21 pages. Several changes are made according to the referee's suggestions

References in corpus (1)

• A Global Torelli Theorem for Calabi-Yau Manifolds

Cited by in corpus (3)

• Solving equations with Hodge theory
• New proofs of the Torelli theorems for Riemann surfaces
• Quantum Correction and the Moduli Spaces of Calabi-Yau Manifolds