Seminar| Institute of Mathematical Sciences
Time: Thursday, July 13rd, 2023 , 16:00-17:00
Abstract: Gravitational instantons, which are 4-dimensional complete Ricci-flat manifolds with finite energy, have their origins in physics. Hyperkähler gravitational instantons have been extensively studied and have been completely classified in recent years. It has been discovered that hyperkähler gravitational instantons are always asymptotic to specific model geometries at infinity, namely ALE, ALF, ALG, ALH, and two exceptional cases ALG*, ALH*. While there are only a few known examples of non-Kähler ALF gravitational instantons, it has been conjectured that there are no non-Kähler ALE gravitational instantons. In this presentation, I will discuss results related to ALE gravitational instantons and demonstrate that there are no Hermitian non-Kähler ALE gravitational instantons when the structure group is contained in SU(2).