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...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
2002
|
| _version_ | 1826293752349589504 |
|---|---|
| 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. |
| first_indexed | 2024-03-07T03:35:00Z |
| format | Journal article |
| id | oxford-uuid:bbfbcc1b-e6c6-4e68-97ef-dcbb459f81dd |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:35:00Z |
| publishDate | 2002 |
| record_format | dspace |
| 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 |