If all geodesics are closed on the projective plane

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dc.creatorPries, Christian
dc.date2007-10-04
dc.date.accessioned2026-07-07T08:34:07Z
dc.date.available2026-07-07T08:34:07Z
dc.descriptionThe paper shows that the curvature of RP2 is constant iff all geodesics are closed. Therefore RP2 is the first known manifold with only one G-structure. It took quiete a long time to find such a manifold. The author shows only that if all geodesics are closed then there are infinitely many simple closed geodesics. This proof is based on the geodesic return map and the theory of topological dynamics. From important results of Green, Grove and Gromoll one can conclude the theorem.
dc.description11 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0710.0951
dc.identifierhttp://arxiv.org/abs/0710.0951
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139322
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.subject54H20; 53C10
dc.titleIf all geodesics are closed on the projective plane
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