Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 079, 19 pages      arXiv:2306.11110      https://doi.org/10.3842/SIGMA.2023.079
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

About a Family of ALF Instantons with Conical Singularities

Olivier Biquard a and Paul Gauduchon b
a) Sorbonne Université and Université Paris Cité, CNRS, IMJ-PRG, F-75005 Paris, France
b) École Polytechnique, CNRS, CMLS, F-91120 Palaiseau, France

Received June 21, 2023, in final form October 10, 2023; Published online October 20, 2023

Abstract
We apply the techniques developed in our previous article to describe some interesting families of ALF gravitational instantons with conical singularities. In particular, we completely understand the 5-dimensional family of Chen-Teo metrics and prove that only 4-dimensional subfamilies can be smoothly compactified so that the metric has conical singularities.

Key words: gravitational instantons; toric geometry; conformally Kähler metrics.

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