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Calabi-Yau spacesA Calabi-Yau manifold is a compact Kähler manifold with a vanishing first Chern class, or (equivalently) which is Ricci flat (by Yau's theorem).Calabi-Yau manifolds of complex dimension three (i.e. dimension six) appear in (supersymmetric) string theory compactifications to four dimensions. That is, ten conjectural dimensions in string theory are supposed to come as four of which we are aware, carrying some kind of fibration with fiber dimension six. 
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Calabi-Yau spaces".