Mirror symmetry and self-dual manifolds

Details Mirror symmetry and self-dual manifolds Mirror symmetry and self-dual manifolds

2002-02-02

arxiv.org/abs/math/0202016v1

Mathematics

Differential Geometry

22 pages

Scientific paper

We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"{a}hler 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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