A Calabi–Yau manifold, or 'Calabi–Yau space', is a special type of manifold. It is described in certain branches of mathematics such as algebraic geometry.
The Calabi–Yau manifold's properties, such as Ricci flatness, have applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime might take the form of a 6-dimensional Calabi–Yau manifold. This led to the idea of string theory mirror symmetry.