Zoll Manifolds and Complex Surfaces
微分几何
2007-05-23 v1 复变函数
摘要
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.
引用
@article{arxiv.math/0211021,
title = {Zoll Manifolds and Complex Surfaces},
author = {Claude LeBrun and L. J. Mason},
journal= {arXiv preprint arXiv:math/0211021},
year = {2007}
}