Geometry and topology · Oct 6, 2026
Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds
Proves that every smooth Riemannian metric on Sn, n ≥ 2, has infinitely many prime closed geodesics with pairwise distinct images. The same conclusion holds on every closed manifold admitting a finite smooth spherical cover and on every closed three-manifold, without orientability or nondegeneracy restrictions.
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