Hyper-Kähler quotients of solvable Lie groups

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

JOURNAL OF GEOMETRY AND PHYSICS

Elsevier

Lugar: Amsterdam; Año: 2006 vol. 56 p. 691 - 711

0393-0440

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