Timeline for Existence of Fermi coordinates on a Riemannian manifold
Current License: CC BY-SA 2.5
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| Mar 19, 2010 at 15:28 | comment | added | Anton Petrunin | Your condition is equivalent to bound on curvature at one point. It is outside of arbitrary nbhd of $p$ you space can be arbitrary bad --- you need a global condition, a bound on curvature in a fixed nbhd of $p$ will do. The topological condition will not help either, you may construct a metric on the plane which looks like cylinder in a nbhd of a point and has arbitrary small curvature everywhere. | |
| Mar 19, 2010 at 7:05 | comment | added | Tom LaGatta | Anton: Could you expand on this? By the way, my manifold is topologically equivalent to the plane, so there are no topological obstructions as with the torus. What do you mean by "make this bound to be uniform on the manifold?" | |
| Mar 19, 2010 at 2:33 | history | answered | Anton Petrunin | CC BY-SA 2.5 |