Timeline for Are isometries the only geodesic preserving maps in a CAT(0)-space?
Current License: CC BY-SA 2.5
4 events
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| Feb 19, 2010 at 19:59 | comment | added | HenrikRüping | Applying (x,y)->(x+y,y) gives a geodesic, which is not parametrized by unit speed and hence the map is not compatible with s . Maybe I misunderstood how affine maps on R² should extend to this space. Hence also in this example there are only self-similarities. | |
| Feb 19, 2010 at 19:58 | comment | added | HenrikRüping | We can take any one point union of Euclidean spaces to get a self-similar spaces. Note that then the only affine maps are these self-similarities. But I think there is a problem with the "forest". If I consider the geodesic, which goes first from (0,0) to (1,0) and then one up (in the direction of the half line). I guess the idea is, that every affine map of R² extends to a map of this space by preserving the distance in the attached directions. | |
| Feb 19, 2010 at 14:40 | comment | added | Greg Kuperberg | Indeed, if you stitch together any collection of Euclidean spaces in a tree-like fashion, it will be a counterexample. | |
| Feb 19, 2010 at 14:33 | history | answered | Guntram | CC BY-SA 2.5 |