A Kummer Construction for Gravitational Instantons

Olivier Biquard (1, 2) , Vincent Minerbe (3, 1)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat Kähler metrics asymptotic to the product of a real line with a flat 3-manifold.

Domaines: Géométrie différentielle [math.DG]; Physique mathématique [math-ph]

Olivier Biquard, Vincent Minerbe. A Kummer Construction for Gravitational Instantons. Communications in Mathematical Physics, 2011, 308 (3), pp.773-794. ⟨10.1007/s00220-011-1366-y⟩. ⟨hal-02928852⟩