OpenAI reports infinitely many closed geodesics on every Riemannian sphere
- Mathematics
Every smooth Riemannian metric on the standard sphere Sⁿ, for n≥2, has infinitely many prime closed geodesics with pairwise distinct images.
OpenAI reports infinitely many closed geodesics on every Riemannian sphere
- Mathematics
Every smooth Riemannian metric on the standard sphere Sⁿ, for n≥2, has infinitely many prime closed geodesics with pairwise distinct images.
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Understand the problem ↓Understanding the problem
Read the background
Every smooth Riemannian metric on the standard sphere Sⁿ, for n≥2, has infinitely many prime closed geodesics with pairwise distinct images.
Why it matters
If correct, resolves the sphere case of the closed-geodesic infinitude problem for all smooth metrics.
What counts as progress
Does every smooth Riemannian sphere have infinitely many distinct closed geodesic images?
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OpenAI reports infinitely many closed geodesics on every Riemannian sphere