it is a hypercomplex manifold. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds. Hyperkähler manifolds were defined by Eugenio...

uniqueness theorem for hyperkähler metrics on compact Kähler manifolds admitting holomorphically symplectic structures. Examples of hyperkähler metrics on noncompact...

manifold G2 manifold Kähler manifold Calabi–Yau manifold Hyperkähler manifold Quaternionic Kähler manifold Riemannian symmetric space Spin(7) manifold The Wikibook...

K3 surface is Kähler (by Siu). Almost complex manifold Hyperkähler manifold Quaternion-Kähler manifold K-energy functional Cannas da Silva (2001), Definition...

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

compact complex tori, K3 surfaces are the Calabi–Yau manifolds (and also the hyperkähler manifolds) of dimension two. As such, they are at the center of...

describes a field Σ which takes on values in a nonlinear manifold called the target manifold  T. The non-linear σ-model was introduced by Gell-Mann &...

super-space extensions, was developed by J. Harnad and S. Shnider. Hyperkähler manifolds of dimension 4 k {\displaystyle 4k} also admit a twistor correspondence...

mathematics, the hyperkähler quotient of a hyperkähler manifold acted on by a Lie group G is the quotient of a fiber of a hyperkähler moment map M → g...

In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind...

connected self-dual Einstein 4-manifolds are coincide with the 4-dimensional, reverse-oriented hyperkähler manifolds in the Ricci-flat case, but are...

Forms and Geometric Invariants," from which the theory arose. Given a manifold and a Lie algebra valued 1-form A {\displaystyle \mathbf {A} } over it...

Calabi–Yau manifold into simpler pieces and considering the effects of T-duality on these pieces. The simplest example of a Calabi–Yau manifold is a torus...

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...

Roger; Dancer, Andrew S. (2000), "The geometry and topology of toric hyperkähler manifolds" (PDF), Communications in Analysis and Geometry, 8 (4): 727–760...

complex Lagrangian submanifolds of hyperkähler manifolds, fixed points of a real structure of Calabi–Yau manifolds. The SYZ conjecture deals with the...

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...

algebraic surfaces, and via the ADHM construction, or hyperkähler reduction (see hyperkähler manifold), a geometric invariant theory procedure. The groundbreaking...

and Andrew Neitzke, which used physical ideas to derive new results in hyperkähler geometry. Another realization of the AdS/CFT correspondence states that...

}_{2}} . Although the above loose version of the definition includes hyperkähler manifolds, the standard convention of excluding these will be followed by...

SO(4n), so every hyperkähler manifold is a Calabi–Yau manifold, every Calabi–Yau manifold is a Kähler manifold, and every Kähler manifold is orientable....

In differential geometry, a G2 manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G...

sheaves on one Calabi–Yau manifold is equivalent in a certain sense to the Fukaya category of a completely different Calabi–Yau manifold. This equivalence provides...

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

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...

Generalized complex manifold Calabi–Yau manifold Hyperkähler manifold K3 surface hypercomplex manifold Quaternion-Kähler manifold Symplectic topology...

is essentially a hyperkähler manifold with an extra U(1) symmetry. (In general, Gibbons–Hawking metrics are a subclass of hyperkähler metrics.) Gibbons–Hawking...

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...