In mathematics, the hyperkähler quotient of a

hyperkähler manifold In differential geometry, a hyperkähler manifold is a Riemannian manifold (M, g) endowed with three integrable almost complex structures I, J, K that are Kähler with respect to the Riemannian metric g and satisfy the quaternionic relations I^2 ...

acted on by a

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

''G'' is the quotient of a fiber of a hyperkähler moment map

M \to \mathfrak \otimes \mathbb^3

over a ''G''-fixed point by the action of ''G''. It was introduced by

Nigel Hitchin Nigel James Hitchin FRS (born 2 August 1946) is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of O ...

, Anders Karlhede,

Ulf Lindström Ulf Lindström (born 12 November 1947) is a Swedish theoretical physicist working in the fields of string theory, supersymmetry, and general relativity. He earned his fil. kand. university degree at Stockholm University in 1972 and continued un ...

, and Martin Roček in 1987. It is a hyperkähler analogue of the Kähler quotient.

References

* Differential geometry {{differential-geometry-stub