2 results
From ALE to ALF gravitational instantons
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 6 / June 2018
- Published online by Cambridge University Press:
- 03 May 2018, pp. 1159-1221
- Print publication:
- June 2018
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In this article, we give an analytic construction of ALF hyperkähler metrics on smooth deformations of the Kleinian singularity
$\mathbb{C}^{2}/{\mathcal{D}}_{k}$, with 
${\mathcal{D}}_{k}$ the binary dihedral group of order 
$4k$, 
$k\geqslant 2$. More precisely, we start from the ALE hyperkähler metrics constructed on these spaces by Kronheimer, and use analytic methods, e.g. resolution of a Monge–Ampère equation, to produce ALF hyperkähler metrics with the same associated Kähler classes.
BIHERMITIAN STRUCTURES ON COMPLEX SURFACES Proc. London Math. Soc. (3) 79 (1999) 414–428)
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- Journal:
- Proceedings of the London Mathematical Society / Volume 92 / Issue 1 / January 2006
- Published online by Cambridge University Press:
- 19 December 2005, pp. 200-202
- Print publication:
- January 2006
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