  This paper considers the natural geometric structure on the moduli space of
deformations of a compact special Lagrangian submanifold $L^n$ of a Calabi-Yau
manifold. From the work of McLean this is a smooth manifold with a natural
$L^2$ metric. It is shown that the metric is induced from a local
  Lagrangian immersion into the product of cohomology groups $H^1(L)\times
H^{n-1}(L)$. Using this approach, an interpretation of the mirror symmetry
discussed by Strominger, Yau and Zaslow is given in terms of the classical
Legendre transform.
