M. L. Barberis, I. Dotti, A. Fino
Hyper-Kähler quotients of solvable Lie groups
The paper is published: J. Geom. Phys. 56 (4) (2006) 691-711

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

53C55 Hermitian and Kahlerian manifolds, See also {32Cxx}

22E25 Nilpotent and solvable Lie groups

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

Abstract: 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.