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Manifolds with holonomy \(U^*(2m)\)

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Abstract

We consider the geometry determined by a torsion-free affine connection whose holonomy lies in the subgroup \(U^*(2m)\), a real form of \(GL(2m,\mathbf {C})\), otherwise denoted by \(SL(m,\mathbf {H}) \cdot U(1)\). We show in particular how examples may be generated from quaternionic Kähler or hyperkähler manifolds with a circle action.

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  1. Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK

    Nigel Hitchin

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  1. Nigel Hitchin
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Hitchin, N. Manifolds with holonomy \(U^*(2m)\) . Rev Mat Complut 27, 351–368 (2014). https://doi.org/10.1007/s13163-014-0150-x

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