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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In Infinitely many closed geodesic images on every Riemannian sphere, 24 September 2026
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For every integer n\ge2 and every smooth Riemannian metric on the standard smooth sphere S^n, there are infinitely many prime closed geodesics with pairwise different images.
In Infinitely many closed geodesic images on every Riemannian sphere, 24 September 2026
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Let N be a closed manifold admitting a finite smooth cover diffeomorphic to a standard sphere S^n, where n\ge2. Every smooth Riemannian metric on N has infinitely many geometrically distinct prime closed geodesics.
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Why this passage is shown
Theorem 1.1
In Infinitely many closed geodesic images on every Riemannian sphere, 24 September 2026
Why this passage is shown
Corollary 1.2
In Infinitely many closed geodesic images on every Riemannian sphere, 24 September 2026
Why this passage is shown
Corollary 1.3 (Closed three-manifolds)
In Infinitely many closed geodesic images on every Riemannian sphere, 24 September 2026