Let $\omega$ be a Kähler form on $X_{U}$, $\omega_{SF}$ the semi-flat Kähler form on $X_{0}$, such that

$$\int_{X_{b}}\omega=\int_{X_{b}}\omega_{SF}=\epsilon.$$

Then $[\omega_{SF}-\omega]=0$ in $H^{2}(X_{U^{*}},{\bf R})$, and furthermore, there exists a holomorphic section $\sigma$ of $f:X_{U}\rightarrow U$ and a function $\varphi$ on $X_{U^{*}}$ such that

$$\omega_{SF}-T_{\sigma}^{*}\omega=i\partial\bar{\partial}\varphi,$$

where $T_{\sigma}$ is translation by the section $\sigma$.