Closed geodesic
Summary
A closed geodesic on a Riemannian manifold is a geodesic that closes up smoothly, returning to its starting point with its starting velocity. Equivalently, it is a nonconstant critical point of the energy on the space of closed loops. Closed geodesics are the periodic orbits of the geodesic flow. Their existence and their number are central questions of the variational theory of geodesics and of Hamiltonian dynamics.
Where this leads
5 pages build on this one.
Further reading
About this page
| Tag | 4MCCP8GG4J |
|---|---|
| URI | m2://4MCCP8GG4J |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53C22, 58E10 |
| Specializes | Geodesic |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Results about this
- Theorem of the three geodesics
- Lyusternik–Fet theorem
- Bangert–Franks theorem on closed geodesics on the sphere
- Gromoll–Meyer theorem on closed geodesics
Used by
- Theorem of the three geodesics
- Lyusternik–Fet theorem
- Birkhoff min-max method
- Bangert–Franks theorem on closed geodesics on the sphere
- Gromoll–Meyer theorem on closed geodesics