I will begin with some basic notions in 4-dimensional Riemannian geometry in order to define the concept of half-conformally-flat metrics (which are also known as self-dual or anti-self dual metrics), and a generalization of these known as Bach-flat metrics. These equations are elliptic in a suitable gauge, and I will discuss a basic regularity theorem.I will also discuss volume growth and Cheeger-Gromov convergence of such metrics, and discuss some explicit examples.
For the timetable and related documents, go to the main page of the trimester "Geometric Flows and Geometric Operators" at cvgmt.sns.it/GFO
http://cvgmt.sns.it/event/127/
