Calabi–Yau manifold
Overview
Compact Kähler manifolds with vanishing first Chern class. Calabi (1954) conjectured existence; Yau (1977) proved it. Central to string theory (compactification) and mirror symmetry.
Era: 1954–1977
Proposed at: Princeton, USA
Formal structure
Domain: Complex manifold M, dim_ℂ M = n; Kähler metric g
c_1(M) = 0; Ricci-flat: Ric(g) = 0; ∃ unique Kähler class [ω]
Constraints: Compact; Kähler; holonomy ⊂ SU(n) (for simply connected)
Objective: String compactification; mirror symmetry; enumerative geometry