Calabi–Yau manifold

Summary

A Calabi–Yau manifold is a compact Kähler manifold with trivial canonical bundle. By Yau's proof of the Calabi conjecture, each Kähler class on it contains a Ricci-flat Kähler metric. Calabi–Yau manifolds sit between Fano varieties and varieties of general type in the classification of varieties. They are central in string theory and in mirror symmetry.