Timeline for $(M,g)$ is complete iff $(\tilde{M},\tilde{g})$ is complete (non-Riemannian version)
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 13, 2019 at 16:19 | vote | accept | user450093 | ||
| Feb 13, 2019 at 16:07 | history | edited | Ben McKay | CC BY-SA 4.0 |
changed frame bundle to tangent bundle to make it clearer
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| Feb 13, 2019 at 15:58 | comment | added | Ben McKay | You could view the geodesic flow as a flow on $TM$ instead of the frame bundle; that will work just as well, with the same proof as above, just replacing the expression frame bundle by the expression $TM$. The geodesic vector field on $TM$ is the vector field whose flow is the geodesic flow. | |
| Feb 13, 2019 at 15:20 | comment | added | user450093 | There are some things I don't understand (yet): I know how one can lift a diffeomorphism of $M$ to a diffeomorphism of the frame bundle of $M$, but how do you lift the geodesic flow of $TM$ to the frame bundle? And by geodesic vector field you mean the vector field of this geodesic flow of the frame bundle, right? Is there maybe a reference in which the geodesic flow on the frame bundle of a pseudo-Riemannian manifold is defined? | |
| Feb 13, 2019 at 14:28 | history | answered | Ben McKay | CC BY-SA 4.0 |