Timeline for Is there a coordinate-free proof of the hamiltonian character of the geodesic flow?
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| Feb 27, 2018 at 21:39 | comment | added | Tyson | This follows simply from the fact that levi civita connection is defined in such a way that the energy integrals over geodesics be stationary. Hamiltionian vector fields are time flows of sympletic manifolds given by the principle of extreme action. If your action consists only of the hamiltonian in question, extremizing it will give geodesics as integral curves of the hamiltonian vector field. | |
| Feb 17, 2012 at 8:30 | comment | added | Sebastian | Dear Giuseppe, I am sorry that I don't know any good reference for this, but the part concerning horizontal bundles is contained in a book of Michor,.., you can find it here: emis.de/monographs/KSM/kmsbookh.pdf | |
| Feb 16, 2012 at 18:32 | comment | added | agt | Dear Sebastian, thank you. Would you suggest me some readings following the same line of your exposition? | |
| Feb 16, 2012 at 15:34 | history | answered | Sebastian | CC BY-SA 3.0 |