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Hyper-Kähler quotients of solvable Lie groups

M. L. Barberis·I. Dotti·A. Fino
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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 $\H^p \times \H^q$ ($\H$: the quaternions). We obtain new complete hyper-Kähler metrics on Euclidean spaces and give their local expressions.

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BibTeXRIS

M. L. Barberis, I. Dotti, A. Fino. 2004-11-13. Hyper-Kähler quotients of solvable Lie groups. https://arxiv.org/abs/math/0411307

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