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  "body": "\n## Summary\n\nA Calabi–Yau manifold is a compact [[Kähler manifold|X60JG9AEQJ]] with trivial canonical bundle.\nBy Yau's proof of the [[Calabi conjecture|WJKA5YBTJ7]], each Kähler class on it contains a Ricci-flat Kähler metric.\nCalabi–Yau manifolds sit between Fano varieties and varieties of general type in the classification of varieties.\nThey are central in string theory and in [[mirror symmetry|YK3DMN2NSK]].\n\n## Explanations\n\n### L1 human\n\nThe canonical bundle measures how a complex manifold curves on average, and on a Calabi–Yau manifold it is trivial, so the manifold is flat on average.\nIn complex dimension $1$ the Calabi–Yau manifolds are the elliptic curves, which are tori.\nIn dimension $2$ the simply connected ones are the K3 surfaces.\nA smooth quintic hypersurface in $\\mathbb{P}^4$ is a Calabi–Yau threefold, and it is the most studied example in physics.\n",
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