Mirror symmetry and self-dual manifolds
Abstract
We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"ahler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the existence of a transformation similar to the Fourier-Mukai functor, suggest that this approach may be able to explain mirror symmetry also in other situations
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