Reputation
Top tag
dg.differential-geometry
Aug
4 |
awarded | Nice Answer |
Jul
5 |
awarded | Good Answer |
Jul
4 |
awarded | Yearling |
May
12 |
awarded | Nice Question |
May
11 |
comment |
What sort of models did Bolyai and Lobachevsky use to demonstrate the consistency of their models of non-Euclidean Geometry?
>... but neither Bolyai nor Lobachevsky proved that their geometry was internally consistent... That's what I was beginning to suspect, Igor, but is that something that is "As far as I know...", or do you have some strong reason to believe this---say perhaps a well-researched historical reference. |
May
11 |
asked | What sort of models did Bolyai and Lobachevsky use to demonstrate the consistency of their models of non-Euclidean Geometry? |
Apr
30 |
awarded | Nice Answer |
Apr
19 |
awarded | Great Answer |
Jan
11 |
answered | Characterization of the exterior derivative |
Sep
30 |
awarded | Explainer |
Sep
29 |
awarded | Nice Answer |
Jul
4 |
awarded | Yearling |
Jul
2 |
awarded | Curious |
May
24 |
awarded | Enlightened |
May
24 |
awarded | Nice Answer |
Feb
3 |
awarded | Nice Question |
Nov
18 |
awarded | Good Answer |
Nov
2 |
awarded | Popular Question |
Sep
30 |
comment |
About Palais' remark that an isometry of Riemannian manifolds does not induce an isometry of the Hilbert manifolds of curves
The problem lies in the line above defining $g_\sigma(λ,μ)$. This is the metric for $H_0$, NOT the metric for $H_1$. The correct definition of the metric for $H_1$ uses $⟨λ'(t),μ'(t)⟩$ rather than $⟨λ(t),μ(t)⟩$ (see page 222 of my article where both metrics are defined), and with this change it is fairly obvious why my remark in the cited paper is in fact correct. |
Aug
23 |
comment |
Algorithm for finding inverse images of a local diffeomorphism
Yes! Newton's Method is clearly the way to go. For $k=1$, the algorithm I wrote in fact did use Newton's Method, (rather than bisection) since it is much faster. But I guess I forgot that Newton's Method works in higher dimensions too. Thanks Ryan. |