The moduli space of special Lagrangian submanifolds

Details The moduli space of special Lagrangian submanifolds The moduli space of special Lagrangian submanifolds

1997-11-04

arxiv.org/abs/dg-ga/9711002v1

Annali Scuola Sup.Norm.Pisa Sci.Fis.Mat. 25 (1997) 503-515

Mathematics

Differential Geometry

14 pages

Scientific paper

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.

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