Timeline for A connection on $Hom( E,E)$ whose parallel transport is compatible to parallel transport of $E$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2016 at 20:34 | comment | added | Robert Bryant | Yes, certainly. | |
| Jul 4, 2016 at 18:38 | comment | added | Ali Taghavi | @RobertBryant Thank you very much for your comment. And the Riemannian property would be preserved? | |
| Jul 4, 2016 at 17:21 | comment | added | Robert Bryant | Perhaps it should be pointed out that this is a special case of a more general fact: Each connection $\nabla$ on $E$ induces a canonical connection $\nabla^{r,s}$ on $E^{\otimes r}\otimes (E^*)^{\otimes s}$ that is compatible with all tensor products, contractions, sub-representations, etc., so all of the parallel transports are also compatible. Your case is just $(r,s)=(1,1)$. | |
| Jul 4, 2016 at 13:40 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
deleted 10 characters in body
|
| Jul 4, 2016 at 13:32 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 112 characters in body
|
| Jul 4, 2016 at 11:34 | comment | added | Ali Taghavi | @Ben thank you for your edit. It seems that we were editing simultanously. In my new edit I fix my errors you pointed out. | |
| Jul 4, 2016 at 10:39 | answer | added | Sebastian | timeline score: 2 | |
| Jul 4, 2016 at 9:58 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 71 characters in body; edited title
|
| Jul 4, 2016 at 9:56 | history | edited | Ben McKay | CC BY-SA 3.0 |
spelling, grammar, formatting
|
| Jul 4, 2016 at 9:53 | history | asked | Ali Taghavi | CC BY-SA 3.0 |