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| Calabi-Yau Manifold as it would appear in 3D |
Calabi-Yau manifolds are compact, complex Kähler manifolds that have trivial first Chern classes (over R). In most cases, we assume that they have finite fundamental groups. By the conjecture of Calabi (1957) proved by Yau (1977; 1979), there exists on every Calabi-Yau manifold a Kähler metric with vanishing Ricci curvature. (Scholarpedia)
Wikipedia Link: Manifolds
Scholarpedia Link: Calabi-Yau Manifold
Wolfram Link: Calabi-Yau Space
Physics arXiv: Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons and Mirror Symmetry
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