Calabi-Yau manifold | Calabi-Yau variety

Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form M×V, where M is a four dimensional manifold (space-time) and V is a six dimensional compact Calabi-Yau space. They are related to Kummer surfaces. Although the main application of Calabi-Yau spaces is in theoretical physics, they are also interesting from a purely mathematical standpoint. Consequently, they go by slightly different names, depending mostly on context, such as Calabi-Yau manifolds or Calabi-Yau varieties.

canonical bundle | complex manifold | harmonic | Kähler form | Lie group | mirror pair | moduli space | spinor | variety