Hyper-kahler quotients of solvable Lie gropus

M.L.BARBERIS, I.DOTTI, A.FINO

JOURNAL OF GEOMETRY AND PHYSICS

Elsevier

Año: 2006 vol. 56 p. 691 - 711

0393-0440

 In this paper we apply the   hyper-K"ahler quotient construction to Lie groups with a left invariant hyper-K"ahlerstructure under the action ofa 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 consideringdifferent Lie group structures on H^p x  H^q (H: thequaternions). We obtain new complete hyper-K"ahler metrics on Euclidean spaces and give their local expressions.