AbstractUnless it is a flat connection, an affine connection cannot be at the same time projectively flat (geodesics being straight lines) and conformal (conformal structure being preserved by parallel transport). This impossibility is examplified by the two standard models of hyperbolic geometry: Beltrami and Poincaré models. We define stiff connections by weakening the conformality hypothesis...
AbstractWe will introduce the general twistor space picture for moduli spaces of connections deforming to moduli spaces of Higgs bundles, initiated by Hitchin for his hyperkähler structure. The Deligne-Hitchin twistor space construction has a property analogous to weight 1 Hodge structures.This may be extended to twistor structures of other weights. In the case of moduli theory of connections o...