Instantons on quaternionic Kähler manifolds and prepotentials

17.05.2019, 10:30 Uhr  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Andrea Spiro (Università di Camerino)

An instanton on a quaternionic Kähler manifold is a connection on a principle bundle, whose  curvature is pointwise adapted to the quaternionic structure of the tangent space. 

These instantons are special solutions to the Yang-Mills equations and are natural generalisations of the  anti-self-dual solutions to the Yang-Mills equations on S⁴, fully classified by Atiyah-Drinfeld-Hitchin-Manin in the '80s. 
We are going to present a novel approach which provides a complete (local) description of each instanton on a quaternionic Kaehler manifold in terms of a single complex function, the prepotential. 
This approach yields radical simplifications and immediate generalisations of important results like Uhlenbeck's Compactness Theorem for Yang-Mills fields.