Quasi-isometry and deformations of Calabi–Yau manifolds

By Kefeng Liu, S. Rao, Xiaokui Yang. 2012

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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 $$(n,0)$$(n,0)-forms on the deformation spaces of Calabi–Yau manifolds. Similar constructions are also applied to the deformation spaces of compact Kähler manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/250ad914c19dc049491b157db1437f1143f93bd7