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July, 2002 Zoll Manifolds and Complex Surfaces
Claude Lebrun, L.J. Mason
J. Differential Geom. 61(3): 453-535 (July, 2002). DOI: 10.4310/jdg/1090351530

Abstract

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 [4] 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.

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

Information

Published: July, 2002
First available in Project Euclid: 20 July 2004

zbMATH: 1070.53022
MathSciNet: MR1979367
Digital Object Identifier: 10.4310/jdg/1090351530

Rights: Copyright © 2002 Lehigh University

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