Closed geodesics on geodesic spaces of curvature \(<\infty\) (Q1987047)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Closed geodesics on geodesic spaces of curvature \(<\infty\) |
scientific article; zbMATH DE number 7188964
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Closed geodesics on geodesic spaces of curvature \(<\infty\) |
scientific article; zbMATH DE number 7188964 |
Statements
Closed geodesics on geodesic spaces of curvature \(<\infty\) (English)
0 references
9 April 2020
0 references
The existence of a nontrivial closed geodesic was proved in previous works, first for any analytic convex surface, later for any surface of genus zero, further for any closed Riemannian manifold. In the present paper, the existence of a nontrivial closed geodesic is proved for any compact, connected, noncontractible geodesic space with curvature \(<\infty\). It is well explained with easy examples showing that all assumptions in the statement are necessary.
0 references
closed geodesic
0 references
geodesic space
0 references
bounded curvature
0 references
