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

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.

Local extensions of bm$d_H$-closed real forms of pure type on compact generalized Hermitian manifolds

“…The method we used is parallel to that in [22] which originally came from [28,27,5,15,25,26,31,32,21,17]. This is also an extension of local extensions of canonical forms in [30].…”