In local canonical coordinates $y_{i},\check{x}_{i}$ on $\mathcal{T}^{*}_{B}$, the complex coordinate functions $z_{j}=\check{x}_{j}+i\partial K/\partial y_{j}$ on $\mathcal{T}^{*}_{B}$ induce a well-defined complex structure on $\check{X}(B)$, with respect to which the canonical symplectic form $\omega$ is the Kähler form of a metric. Furthermore this metric is Ricci-flat if and only if $K$ satisfies the real Monge-Ampère equation