A number of interesting geometric objects in conformal differential geometry are described by overdetermined differential equations, in particular infinitesimal symmetries, conformal Killing forms/tensors, twistor spinors and Einstein scales. Uniform descriptions of these equations and natural prolongation methods have made it possible to apply tools from differential geometry and representation theory to study solutions. In the present talk I will lay out how the existence of solutions is intimately related to holonomy reductions in conformal geometry and how Lie group techniques can be applied to obtain detailed information about singularity sets. On the other hand, I will discuss how curvatures of prolongation connections can be employed to derive obstructions against the existence of solutions.
14.10.2016