This paper considers the natural geometric structure on the moduli space of
deformations of a compact special Lagrangian submanifold Ln of a Calabi-Yau
manifold. From the work of McLean this is a smooth manifold with a natural
L2 metric. It is shown that the metric is induced from a local
Lagrangian immersion into the product of cohomology groups H1(L)×Hn−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.Comment: 14 page