Differential Geometry and Topology

course: Introduction to extremal Kaehler metrics

speaker: Paul Gauduchon (Ecole Polytechnique)

abstract: In the first `pre-conference' lecture, I plan to briefly recall the main properties of Kaehler manifolds in general, and explain what an extremal Kaehler metric is. Time permitting, I shall discuss Calabi's non-trivial examples.

Later, I shall explain why extremal metrics are characterized by the fact that the scalar curvature is a Killing potential, and provide a proof that the isometry group of an extremal metric is a maximal compact subgroup of the group of automorphisms.

I also aim to give a brief description of the Mabuchi metric on the space of Kaehler metrics, to establish the equation of geodesics, to show that this equation can be transformed into a Monge-Ampere equation and to explain why the existence of geodesics between any two points in the space of Kaehler metrics implies the uniqueness of extremal metrics (using arguments of Donaldson and Guan).

timetable:
Mon 6 Sep, 18:15 - 19:15, Sala Conferenze Centro De Giorgi
Tue 7 Sep, 17:00 - 18:00, Sala Conferenze Centro De Giorgi
Wed 8 Sep, 15:30 - 16:30, Sala Conferenze Centro De Giorgi
<< Go back