Timeline for Local geodesics in uniquely geodesic spaces
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 15, 2014 at 11:07 | comment | added | Mikhail Katz | @Teri, Perhaps you should reformulate your question accordingly. | |
| Aug 14, 2014 at 8:15 | comment | added | Teri | Thanks! that's indeed a nice example. I have a vague impression (but haven't worked out any details) that if the space has the additional property that every global geodesic can be uniquely extended to a (locally) geodesic line, then the local geodesics are also unique. If so, this would mean that one cannot have a (complete) Riemannian manifold as an example. | |
| Aug 14, 2014 at 8:09 | vote | accept | Teri | ||
| Aug 12, 2014 at 14:56 | comment | added | Pablo Lessa | Thanks! After looking at chapter 8 I believe you now :). | |
| Aug 12, 2014 at 14:04 | comment | added | Mikhail Katz | books.google.co.il/… | |
| Aug 12, 2014 at 13:42 | comment | added | Pablo Lessa | I don't believe you :). If $\beta_x$ is the minimizing geodesic joining each $x$ on $\alpha$ to $p$. What's the limit of $\beta_x$ when $x$ converges to $q$? Are you saying this goes to $\alpha$? Proof or reference? | |
| Aug 12, 2014 at 13:20 | comment | added | Mikhail Katz | No, $q$ is the "last" point with a unique minimizer. | |
| Aug 12, 2014 at 13:15 | comment | added | Pablo Lessa | Aren't $p$ and $q$ joined by two minimizing geodesics? | |
| Aug 12, 2014 at 13:08 | history | answered | Mikhail Katz | CC BY-SA 3.0 |