If all geodesics are closed on the projective plane

Details If all geodesics are closed on the projective plane If all geodesics are closed on the projective plane

2007-10-04

arxiv.org/abs/0710.0951v1

Mathematics

Differential Geometry

11 pages, 2 figures

Scientific paper

The 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.

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