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In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties...

partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors...

class contains exactly one Ricci-flat metric. These are often called Calabi–Yau manifolds. However, the term is often used in slightly different ways...

these are now known as Calabi–Yau metrics. They have become significant in string theory research since the 1980s. In 1982, Calabi introduced a geometric...

relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically...

extra dimensions are "wrapped" up on themselves, or "curled" up on Calabi–Yau spaces, or on orbifolds. Models in which the compact directions support fluxes...

in 2008. Greene has worked on mirror symmetry, relating two different Calabi–Yau manifolds (concretely relating the conifold to one of its orbifolds)....

notion of a flop-transition is basically the shrinking of a sphere in a Calabi–Yau space to the point of tearing. Based on typical spacetime topology, this...

Bergman space Berkovich space Besov space Borel space Calabi-Yau space Cantor space Cauchy space Cellular space Chu space Closure space Conformal space Complex...

closed forms, then it defines a generalized Calabi-Yau structure and M is said to be a generalized Calabi-Yau manifold. Locally all pure spinors can be...

the Calabi–Yau. In another version of string theory called the topological A-model, the D-branes can again be viewed as submanifolds of a Calabi–Yau manifold...

results to be proven with great success, including Shing-Tung Yau's proof of the Calabi conjecture, the Hitchin–Kobayashi correspondence, the nonabelian...

since both have the same holonomy group. Similarly, the space can also be used to construct Calabi–Yau manifolds by replacing the orbifold singularities of...

manifolds are Ricci-flat and are thus Calabi–Yau manifolds. Hyperkähler manifolds were defined by Eugenio Calabi in 1979. Marcel Berger's 1955 paper on...

compact space formed by rolling up the theory's extra dimensions, specifically a six-dimensional Calabi–Yau space. The simplest viable compact spaces are...

Calabi–Yau compactifications in string theory; this partially supports a conjecture by Reid (1987) whereby conifolds connect all possible Calabi–Yau complex...

SYZ Conjecture: Every 6-dimensional Calabi–Yau manifold X {\displaystyle X} has a mirror 6-dimensional Calabi–Yau manifold X ^ {\displaystyle {\hat {X}}}...

Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location...

latter statement is a consequence of Yau's differential geometric approach which is based on his resolution of the Calabi conjecture. Since c 2 ( X ) = e (...

anew. Landscape The landscape multiverse relies on string theory's Calabi–Yau spaces. Quantum fluctuations drop the shapes to a lower energy level, creating...