Timeline for Does every smooth manifold of infinite topological type admit a complete Riemannian metric?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Mar 20, 2010 at 17:39 | comment | added | Igor Belegradek | Definition of $h$ uses "length", which gives relationship with the metric. I am not claiming $h$ is proper but it could be. | |
| Mar 20, 2010 at 16:44 | comment | added | Harald Hanche-Olsen | Yeah, but is it enough for it to be proper? It seems to me it has to have some relationship with the metric to insure that paths that stray outside of any compact will be infinitely long in the rescaled metric. | |
| Mar 20, 2010 at 16:12 | comment | added | Igor Belegradek | The idea is right I think but your $h$ is unnecessary complicated; there are easier ways to find a proper smooth positive function on a manifold. | |
| Mar 20, 2010 at 16:03 | history | answered | Harald Hanche-Olsen | CC BY-SA 2.5 |