LeBrun, Claude; Mason, L. J. Zoll manifolds and complex surfaces. (English) Zbl 1070.53022 J. Differ. Geom. 61, No. 3, 453-535 (2002). Summary: 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 \(\mathbb CP_2\). Cited in 2 ReviewsCited in 22 Documents MSC: 53C22 Geodesics in global differential geometry 32J15 Compact complex surfaces 53C28 Twistor methods in differential geometry Keywords:compact surfaces; torsion-free affine connections; simple closed curve; twistor × Cite Format Result Cite Review PDF Full Text: DOI arXiv