Journal of Differential Geometry

Zoll Manifolds and Complex Surfaces

Claude Lebrun and L.J. Mason

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.

Article information

Source
J. Differential Geom., Volume 61, Number 3 (2002), 453-535.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090351530

Digital Object Identifier
doi:10.4310/jdg/1090351530

Mathematical Reviews number (MathSciNet)
MR1979367

Zentralblatt MATH identifier
1070.53022

Citation

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


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