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 (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
''G'' is the quotient of a fiber of a hyperkähler moment map
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, and
Martin Roček in 1987. It is a hyperkähler analogue of the
Kähler quotient.
References
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Differential geometry
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