Geometry of neutral metrics in dimesnion four

Abstract

The purpose of this article is to review some recent results on the geometry of neutral signature metrics in dimension four and their twistor spaces. The following topics are considered: Neutral Kähler and hyperkähler surfaces, Walker metrics, Neutral anti-self-dual 4-manifolds and projective structures, Twistor spaces of neutral metrics.

20 pages, invited talk at the Thirty Seventh Spring Connference of the Union of Bulgarian Mathematicians, Borovets, April 2-6, 2008