Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 1

Some results of deformations on compact $H$-twisted generalized Calabi–Yau manifolds

Pages: 131 – 169

DOI: https://dx.doi.org/10.4310/PAMQ.2015.v11.n1.a6

Author

Kang Wei ( Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China)

Abstract

In this paper, we prove several formulas related to Hodge theory, and using them to prove the deformations of a compact $H$-twisted generalized Calabi–Yau manifold are unobstructed and $L^2$ convergence in a fixed neighbourhood in another power series. And if we assume that the deformation is smooth in a fixed neighbourhood, and assume the existence of a global canonical family of deformation, we also construct the global canonical family of the deformations of generalized Kähler manifolds.

Keywords

deformations of complex structures, Hodge theory, Hermitian and Kählerian manifolds, Calabi–Yau manifolds

2010 Mathematics Subject Classification

Primary 32G05. Secondary 14J32, 53C55, 58A14.

Published 1 September 2015