×

Zoll manifolds and complex surfaces. (English) Zbl 1070.53022

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 \(\mathbb CP_2\).

MSC:

53C22 Geodesics in global differential geometry
32J15 Compact complex surfaces
53C28 Twistor methods in differential geometry