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Journal Articles Communications in Mathematical Physics Year : 2023

On toric Hermitian ALF gravitational instantons

Abstract

We give a classification of toric, Hermitian, Ricci flat, ALF Riemannian metrics in dimension 4, including metrics with conical singularities. The only smooth examples are on one hand the hyperKaehler ALF metrics, on the other hand, the Kerr, Taub-NUT and Chen-Teo metrics. There are examples with conical singularities with infinitely many distinct topologies. We provide explicit formulas.
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Dates and versions

hal-03501981 , version 1 (08-12-2022)

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Olivier Biquard, Paul Gauduchon. On toric Hermitian ALF gravitational instantons. Communications in Mathematical Physics, 2023, 399, pp.389-422. ⟨10.1007/s00220-022-04562-z⟩. ⟨hal-03501981⟩
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