Zoll Manifolds and Complex Surfaces

Lebrun, Claude; Mason, L.J.

J. Differential Geom., Tome 60 (2002) no. 1, p. 453-535 / Harvested from Project Euclid

Résumé

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.

Publié le : 2002-07-14
Classification:

@article{1090351530,
     author = {Lebrun, Claude and Mason, L.J.},
     title = {Zoll Manifolds and Complex Surfaces},
     journal = {J. Differential Geom.},
     volume = {60},
     number = {1},
     year = {2002},
     pages = { 453-535},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1090351530}
}

Lebrun, Claude; Mason, L.J. Zoll Manifolds and Complex Surfaces. J. Differential Geom., Tome 60 (2002) no. 1, pp.  453-535. http://gdmltest.u-ga.fr/item/1090351530/