Timeline for Completeness of asymptotically Euclidean manifolds
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 10, 2022 at 19:04 | comment | added | Willie Wong | @RomainGicquaud I don't think it has a standard name in English. Hartman calls (the contrapositive) of the Lemme du Bout as the "extension theorem". Jack Hale's book calls it the "continuation theorem". (This is more an ODE theorem than a geometry one.) | |
| Mar 10, 2022 at 18:55 | vote | accept | user900940 | ||
| Mar 10, 2022 at 18:50 | answer | added | Willie Wong | timeline score: 1 | |
| Mar 10, 2022 at 18:39 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Mar 10, 2022 at 18:03 | comment | added | Romain Gicquaud | Yes. The idea is that the unit tangent bundle is locally compact so if you look at the geodesic flow, if you have an incomplete vector field it must leave any compact (in French this is known as the "lemme du bout" but I could not find the English translation). This can only happen if the geodesic leaves any compact of $\mathbb{R}^3$ and this in turns implies that the length of the geodesic must be infinite, which contradicts incompleteness... | |
| Mar 10, 2022 at 17:57 | comment | added | Thomas Rot | My thoughts are: if a vector field is bounded wrt a metric which is geodesically complete, it is complete. You can to apply this to your situation by looking at the vector field generating the geodesic flow ( on the tangent bundle of R^n) | |
| S Mar 10, 2022 at 16:56 | review | First questions | |||
| Mar 10, 2022 at 18:10 | |||||
| S Mar 10, 2022 at 16:56 | history | asked | user900940 | CC BY-SA 4.0 |