High Quality Content by WIKIPEDIA articles! In mathematics, Calabi–Yau manifolds are complex manifolds that are higher-dimensional analogues of K3 surfaces. They are sometimes defined as compact Kahler manifolds whose canonical bundle is trivial, though many other similar but inequivalent definitions are sometimes used. They were named "Calabi–Yau spaces" by Candelas et al. (1985) after E. Calabi (1954, 1957) who first studied them, and S. T. Yau (1978) who proved the Calabi conjecture that they have Ricci flat metrics. In superstring theory the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry.

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