Given a special Lagrangian fibration $f:M \rightarrow B$ of a Calabi-Yau manifold $M$, one can associate to it two affine structures on the base space $B$. A theorem of Hitchin says that there locally exists a convex function $K$ such that the coordinate system in one affine structure is mapped to the coordinate system in the other affine structure. Is it possible to see this theorem explicitly for elliptic curves and K3 surfaces?

Given a special Lagrangian fibration $f:M \rightarrow B$ of a Calabi-Yau manifold $M$, one can associate to it two affine structures (symplectic and complex) on the base space $B$. A theorem of Hitchin says that there locally exists a convex function $K$ such that the coordinate system in one affine structure is mapped to the coordinate system in the other affine structure via the Legendre transform associated to $K$. Is it possible to see this theorem explicitly for elliptic curves and K3 surfaces? What is K for elliptic curves?

Given a special Lagrangian fibration $f:M \rightarrow B$ of a Calabi-Yau manifold $M$, one can associate to it two affine structures on the base space $B$. A theorem of Hitchen says that there locally exists a convex function $K$ such that the coordinate system in one affine structure is mapped to the coordinate system in the other affine structure. Is it possible to see this theorem explicitly for elliptic curves and K3 surfaces?

Given a special Lagrangian fibration $f:M \rightarrow B$ of a Calabi-Yau manifold $M$, one can associate to it two affine structures on the base space $B$. A theorem of Hitchin says that there locally exists a convex function $K$ such that the coordinate system in one affine structure is mapped to the coordinate system in the other affine structure. Is it possible to see this theorem explicitly for elliptic curves and K3 surfaces?