Zoll Manifolds and Complex Surfaces

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...

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Príomhchruthaitheoirí: LeBrun, C, Mason, L
Formáid: Journal article
Foilsithe / Cruthaithe: 2002
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author LeBrun, C
Mason, L
author_facet LeBrun, C
Mason, L
author_sort LeBrun, C
collection OXFORD
description 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.
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spelling oxford-uuid:bbfbcc1b-e6c6-4e68-97ef-dcbb459f81dd2022-03-27T05:21:05ZZoll Manifolds and Complex SurfacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bbfbcc1b-e6c6-4e68-97ef-dcbb459f81ddSymplectic Elements at Oxford2002LeBrun, CMason, LWe 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.
spellingShingle LeBrun, C
Mason, L
Zoll Manifolds and Complex Surfaces
title Zoll Manifolds and Complex Surfaces
title_full Zoll Manifolds and Complex Surfaces
title_fullStr Zoll Manifolds and Complex Surfaces
title_full_unstemmed Zoll Manifolds and Complex Surfaces
title_short Zoll Manifolds and Complex Surfaces
title_sort zoll manifolds and complex surfaces
work_keys_str_mv AT lebrunc zollmanifoldsandcomplexsurfaces
AT masonl zollmanifoldsandcomplexsurfaces