Hyper-Kähler quotients of solvable Lie groups

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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.
18 pages

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Differential Geometry, Mathematical Physics, 53C26; 22E25; 53D20

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http://salesiana.dossiersoluciones.com/handle/123456789/73226

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411307
 http://arxiv.org/abs/math/0411307

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arXiv