Quasi-isometry and deformations of Calabi-Yau manifolds

Kefeng Liu; Sheng Rao; Xiaokui Yang

Quasi-isometry and deformations of Calabi-Yau manifolds

Differential Geometry 2014-02-18 v2 Algebraic Geometry

Authors: Kefeng Liu , Sheng Rao , Xiaokui Yang

Abstract

We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of K\"ahler 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 K\"ahler manifolds.

Keywords

Calabi-Yau manifolds quasi-isometry deformation theory Hodge theory Kodaira-Spencer-Kuranishi theory Beltrami differentials holomorphic forms

Cite

@article{arxiv.1207.1182,
  title  = {Quasi-isometry and deformations of Calabi-Yau manifolds},
  author = {Kefeng Liu and Sheng Rao and Xiaokui Yang},
  journal= {arXiv preprint arXiv:1207.1182},
  year   = {2014}
}

Comments

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

Quasi-isometry and deformations of Calabi-Yau manifolds

Abstract

Keywords

Cite

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