2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65514We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to previous work, our approach is twistor-theoretic, and depends fundamentally on the fact that, up to biholomorphism, there is only one complex structure on CP2.Differential GeometryComplex Variables53C22; 32G10text