Timeline for Relation of pseudo-torsion with curvature in degenerate plane
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2017 at 20:31 | vote | accept | Ivo Terek | ||
| Oct 13, 2017 at 20:30 | answer | added | Ivo Terek | timeline score: 0 | |
| Apr 9, 2017 at 10:33 | comment | added | Robert Bryant | The difficulty is that the group of symmetries of the 'metric' $\mathrm{d}x^2$ on $\mathbb{R}^2$ is the set of transformations of the form $$\phi(x,y) = \bigl(\pm x + c, f(x,y)\bigr).$$ where $c$ is a constant and $f_y(x,y)$ is nowhere vanishing. In particular, any curve of the form $\bigl(s,g(s)\bigr)$ can be transformed into $(s,0)$ by the symmetry $\phi(x,y) = \bigl(x,y-g(x)\bigr)$. Thus, all curves on which $\mathrm{d}x$ is nonvanishing are locally equivalent under the symmetry group, so there is no local invariant that can distinguish them. | |
| Apr 9, 2017 at 4:27 | history | edited | Ivo Terek | CC BY-SA 3.0 |
added 156 characters in body
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| Apr 9, 2017 at 4:10 | history | asked | Ivo Terek | CC BY-SA 3.0 |