Proposition 2.2 . [02Z2]

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Proposition 2.2.

$K\circ f$ is a (local) Kähler potential on $X(B)$ , defining a Kähler form $\omega=2i\partial\bar{\partial}(K\circ f)$ . This metric is Ricci-flat if and only if $K$ satisfies the real Monge-Ampère equation

\det{\partial^{2}K\over\partial y_{i}\partial y_{j}}=constant.