Speaker
Paul Gauduchon, Ecole Polytechnique
Abstract
A Kähler metric is called extremal if its scalar curvature is a Killing potential, i.e. is the moment relative to the Kähler form of a Hamiltonian Killing vector field; it is called toric extremal if the latter belongs to a maximal, effective Hamiltonian toric action preserving the whole Kähler structure. The presence of such a Kähler structure in the conformal class of a class of four-dimensional gravitational instantons of ALF type, including the Euclidean version of well-known Lorentzian spaces, as well as the one-parameter family of instantons recently discovered by Yu Chen and Edward Teo, plays a prominent role in its eventual complete classification, including a new definition of the Chen–Teo instanton, presented in a recent joint paper with Olivier Biquard.