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An analogue of the Gibbons-Hawking Ansatz for quaternionic K\"ahler spaces. (arXiv:1901.11166v1 [math.DG])
来源于:arXiv
We show that the geometry of $4n$-dimensional quaternionic K\"ahler spaces
with a locally free $\mathbb{R}^{n+1}$-action admits a Gibbons-Hawking-like
description based on the Galicki-Lawson notion of quaternionic K\"ahler moment
map. This generalizes to higher dimensions a four-dimensional construction of
Calderbank and Pedersen of self-dual 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 Ro\v{c}ek, Vafa and Vandoren. 查看全文>>