Timeline for Smoothness of the exponential map at the origin
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2016 at 15:00 | vote | accept | Julien Bernard | ||
| Aug 7, 2014 at 7:34 | comment | added | Julien Bernard | Thank you Jaap Eldering. It did not see before that a constant curve could be considered as a degenerate geodesic curve. | |
| Aug 6, 2014 at 16:52 | history | edited | Jaap Eldering | CC BY-SA 3.0 |
Explain in more detail geodesic flow, and it being well-defined at origin.
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| Aug 6, 2014 at 16:45 | comment | added | Jaap Eldering | @Julien: Why not? The ODE in local coordinates is perfectly well-defined, also for $0 \in T_p M$. Actually, the solution is immediately seen to be the constant curve, or point, $(p,0) \in T M$, hence $\exp_p(0) = p$. | |
| Aug 6, 2014 at 16:23 | comment | added | Julien Bernard | Please, cf. my last answer to Thomas Rot. I think that this argument is correct for every vector in Tp, except the zero vector. Because you cannot write a geodesic equation with zero as initial condition for the tangent vector. | |
| Aug 6, 2014 at 15:44 | history | answered | Jaap Eldering | CC BY-SA 3.0 |