A Calabi–Yau manifold can be defined as a compact Ricci-flat Kähler manifold or equivalently one whose first Chern class vanishes.
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Riemann surfaces, two dimensional manifolds equipped with a complex structure, which are topologically classified by the genus, are an important example of this phenomenon.
The gut and immune system form a complex structure that provides defence against ingested toxins and pathogenic bacteria.
Riemannian manifold | Ghost in the Shell: Stand Alone Complex | Theodore Roosevelt National Wildlife Refuge Complex | manifold | The Chimpanzee Complex | Oedipus complex | Meadowlands Sports Complex | military-industrial complex | Kennedy Space Center Visitor Complex | Goldstone Deep Space Communications Complex | complex | Y-12 National Security Complex | Watergate complex | Mi-2/NuRD complex | Ladd S. Gordon Waterfowl Complex | Faliro Coastal Zone Olympic Complex | Complex (magazine) | Complex | Athens Olympic Sports Complex | Victory Base Complex | Truman Sports Complex | SISD Student Activities Complex | Shree Shiv Chhatrapati Sports Complex | Rizal Memorial Sports Complex | QRS complex | Pureland Industrial Complex | Parque Central Complex | Mitchel Athletic Complex | Manifold | Leoncito Astronomical Complex |
Let be the sheaf of holomorphic functions on the compact connected complex manifold X, then by the maximum principle, global sections are constant, ie.