Hyper-Kähler quotients of solvable Lie groups

Details Hyper-Kähler quotients of solvable Lie groups Hyper-Kähler quotients of solvable Lie groups

2004-11-13

arxiv.org/abs/math/0411307v1

Mathematics

Differential Geometry

18 pages

Scientific paper

In this paper we apply the hyper-K\"ahler quotient construction to Lie groups with a left invariant hyper-K\"ahler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known hyper-K\"ahler metrics can be recovered in this way by considering different Lie group structures on $\H^p \times \H^q$ ($\H$: the quaternions). We obtain new complete hyper-K\"ahler metrics on Euclidean spaces and give their local expressions.

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