Journal of Differential Geometry
- J. Differential Geom.
- Volume 61, Number 3 (2002), 453-535.
Zoll Manifolds and Complex Surfaces
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.
J. Differential Geom., Volume 61, Number 3 (2002), 453-535.
First available in Project Euclid: 20 July 2004
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Lebrun, Claude; Mason, L.J. Zoll Manifolds and Complex Surfaces. J. Differential Geom. 61 (2002), no. 3, 453--535. doi:10.4310/jdg/1090351530. https://projecteuclid.org/euclid.jdg/1090351530