Timeline for A question on Levi-Civita connection and a fixed hyper surface
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2021 at 11:25 | vote | accept | Ali | ||
| Jul 13, 2021 at 2:52 | answer | added | Willie Wong | timeline score: 4 | |
| Jul 13, 2021 at 0:56 | comment | added | Ali | The question can also be posed in Lorentzian setup but I stated it in Riemannian setting for simplicity. | |
| Jul 13, 2021 at 0:55 | comment | added | Ali | $Z$ can be thought of as a vector field on $M$ that when restricted to $\Sigma$, is tangent to $\Sigma$. By the restriction of $D_{\nabla \phi}\nabla \phi$ to $\Sigma$ I mean the restriction, so the equation should be considered on $\Sigma$ only. | |
| Jul 13, 2021 at 0:28 | comment | added | Willie Wong | Additionally, when $Z$ is said to be a smooth vector field on $\Sigma$, do you mean $Z$ is tangent to $\Sigma$, or a vector field of $M$ restricted to $\Sigma$? And when you say "restriction of $D_{\nabla \phi} \nabla \phi$ to $\Sigma$" do you mean the projection, to $T\Sigma$ or just the restriction? | |
| Jul 13, 2021 at 0:26 | comment | added | Willie Wong | Why is this question tagged with lorentzian and semi-riemannian geometry? All the objects in sight seems to be Riemannian. Is there some connection to semi-Riemannian stuff? If so, can you make it explicit? | |
| Jul 12, 2021 at 20:18 | comment | added | Ali | Indeed $f$ is redundant :) | |
| Jul 12, 2021 at 20:13 | comment | added | Leo Moos | The Whitney extension theorem could be relevant. (Also, do you need $f$ at all?) | |
| Jul 12, 2021 at 19:23 | history | asked | Ali | CC BY-SA 4.0 |