Timeline for A consequence of Ambrose-Singer theorem on holonomy
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2020 at 21:44 | vote | accept | Mike Cocos | ||
| Jan 23, 2020 at 18:06 | comment | added | Mike Cocos | @Thank you. I've used the duke email address. Let me know if you'd rather use a different one. | |
| Jan 23, 2020 at 17:28 | comment | added | Robert Bryant | @MikeCocos: Sure. I'd be happy to help if I can. You can email me directly if you don't want to use MO as an intermediary. | |
| Jan 23, 2020 at 16:41 | comment | added | Mike Cocos | Please let me know if I can ask you for some input on a related problem. I am sure it wouldn't take too long for you to spot eventual mistakes but I don't want to take advantage of too much of your time. It is about affinely flat manifolds. Thank you for al your help! | |
| Dec 16, 2019 at 18:15 | comment | added | Mike Cocos | Professor Bryant. No there is no issue with your answer. You are always very helpful and to the point. It is my mind that works really slow. Besides not having enough time to spend on research my mind doesn't help much either. It is clear now to me that the curvature at a single point doesn't contain as much information as the restricted holonomy group. I might not need that much though since all I am looking for is a simple algorithm to determine when a connection is locally metric. Thank you so much for your kind help. | |
| Dec 15, 2019 at 8:02 | comment | added | Robert Bryant | @MikeCocos: You are welcome. Is there something about my answer that you don't believe or understand? If so, let me know, and I'll try to answer your questions. I realize that many people misunderstand the Ambrose-Singer theorem, and your questions seem to stem from one of the common misunderstandings that is often not addressed in treatments of the subject. It's worthwhile to have these kinds of examples out there to help dispel these misconceptions. | |
| Dec 13, 2019 at 16:25 | comment | added | Mike Cocos | I apologize for the ambiguity. Yes my question was if the matrices $S_k(p)$ span the linear algebra of $Hol_p^o(\nabla)$ for all $p \in U.$ Your example answers my question. Thank you! | |
| Dec 13, 2019 at 11:29 | history | edited | Robert Bryant | CC BY-SA 4.0 |
Added a new example, this time one on the tangent bundle and also torsion-free.
|
| Dec 13, 2019 at 7:08 | history | edited | Robert Bryant | CC BY-SA 4.0 |
completed the entry of the counterexample
|
| Dec 13, 2019 at 6:55 | history | edited | Robert Bryant | CC BY-SA 4.0 |
added 898 characters in body
|
| Dec 13, 2019 at 6:09 | history | answered | Robert Bryant | CC BY-SA 4.0 |