Timeline for $L^2$ metric on $\textrm{Diff}(M)$ and geodesics
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2023 at 15:10 | comment | added | Kaira | @RyanBudney The paper isn't really clear about it, but it seems like $M$ is assumed to be compact or closed. For me the case $M=\mathbb{R}^n$ is enough though. | |
| Jan 1, 2023 at 7:47 | comment | added | Ryan Budney | What is the assumption going into your if and only if statement? From the way you write it, I would assume the family $\eta(t)$ are always assumed to be diffeomorphisms. | |
| Dec 31, 2022 at 23:10 | comment | added | Kaira | @RyanBudney Yes, it's about Riemannian metric. $M$ is Riemannian manifold too and $\langle\cdot,\cdot \rangle$ is Riemannian metric on $M$. I should have been clear about it. | |
| Dec 31, 2022 at 23:05 | comment | added | Ryan Budney | Perhaps I don't understand your terminology, but I don't see how the function you've defined could be interpreted as a metric on $Diff(M)$. Presumably you need a function of the form $Diff(M) \times Diff(M) \to \mathbb R$. Aha, you are using "metric" in the sense of Riemann metric? | |
| Dec 31, 2022 at 21:41 | history | asked | Kaira | CC BY-SA 4.0 |