Kähler-Yang-Mills Equations and Vortices

Abstract

The Kähler-Yang-Mills equations are coupled equations for a Kähler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the Kähler-Yang-Mills equations, we consider dimensional reductions of the equations related to vortices - solutions to certain Yang-Mills-Higgs equations.

Paper in honour of Jean-Pierre Bourguignon