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Mirror symmetry is $$T$$-duality. (English) Zbl 0896.14024
Summary: It is argued that every Calabi-Yau manifold $$X$$ with a mirror $$Y$$ admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space $$Y$$. The mirror transformation is equivalent to $$T$$-duality on the 3-cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed.

##### MSC:
 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14M30 Supervarieties 14J30 $$3$$-folds
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