We 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.
"Zoll Manifolds and Complex Surfaces." J. Differential Geom. 61 (3) 453 - 535, July, 2002. https://doi.org/10.4310/jdg/1090351530