2002/11/01 by Claude LeBrun, LeBrun, Claude, L. J. Mason +1
Mathematics · #32G10 #53C22 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32G10 #msc:53C22
paper · pdf · doi:10.48550/arxiv.math/0211021
arxiv created 2002/11/01 · arxiv updated 2009/11/30
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.