Hyperkähler quotient

Short description: Mathematics concept

In differential geometry, 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 $M\to \mathfrak{𝔤}\otimes {\mathbb{ℝ}}^3$ over a G-fixed point by the action of G. It was introduced by Nigel Hitchin, Anders Karlhede, Ulf Lindström, and Martin Roček in 1987. It is a hyperkähler analogue of the Kähler quotient.

References

• Hitchin, N. J.; Karlhede, A.; Lindström, U.; Roček, M. (1987), "Hyper-Kähler metrics and supersymmetry", Communications in Mathematical Physics 108 (4): 535–589, doi:10.1007/BF01214418, ISSN 0010-3616, https://projecteuclid.org/download/pdf_1/euclid.cmp/1104116624