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arXiv · 1901.11166

An analogue of the Gibbons-Hawking Ansatz for quaternionic Kähler spaces

Radu A. Ionas
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Abstract

We show that the geometry of $4n$-dimensional quaternionic Kähler spaces with a locally free $\mathbb{R}^{n+1}$-action admits a Gibbons-Hawking-like description based on the Galicki-Lawson notion of quaternionic Kähler moment map. This generalizes to higher dimensions a four-dimensional construction, due to Calderbank and Pedersen, of self-dual Einstein manifolds with two linearly independent commuting Killing vector fields. As an application, we use this new Ansatz to give an explicit equivariant completion of the twistor space construction of the local c-map proposed by Roček, Vafa and Vandoren.

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Radu A. Ionas. 2019-07-14. An analogue of the Gibbons-Hawking Ansatz for quaternionic Kähler spaces. https://arxiv.org/abs/1901.11166

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