Hyper-Kahler quotients of solvable Lie groups

In this paper we apply the hyper-Kahler quotient construction to Lie groups with a left invariant hyper-Kahler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known hyper-Kahier metrics can be recovered in this way by considering different Lie group structures on H-p x H-q (H: the quaternions). We obtain new complete hyper-Kahler metrics on Euclidean spaces and give their local expressions. (c) 2005 Elsevier B.V. All rights reserved.