Timeline for diagonalizability of the curvature operator
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2011 at 14:37 | comment | added | Willie Wong | @Robert: 1. thanks for the (obvious) correction! 2. You are absolutely correct. I wanted to say something similar to what you wrote, but I wasn't able to phrase it in a way that manifests the restriction clearly. | |
| Nov 14, 2011 at 14:34 | history | edited | Willie Wong | CC BY-SA 3.0 |
added 33 characters in body
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| Nov 14, 2011 at 12:59 | comment | added | Robert Bryant | @Willie: 1. Actually, in your second paragraph, offering the Einstein (anti-)self-dual metrics as non-examples, you have to disallow the round $4$-sphere, which satisfies your conditions but does have this kind of diagonalization. 2. Also, in dimension $4$, the cone of curvature tensors at a point that have this kind of diagonalization has codimension 8 in the $20$-dimensional space of all curvature tensors at a point. Thus, having such a diagonalization, even at one point, is quite restrictive in dimension $4$. It only gets more restrictive in higher dimensions. | |
| Nov 10, 2011 at 5:04 | vote | accept | atreyee | ||
| Nov 10, 2011 at 5:03 | vote | accept | atreyee | ||
| Nov 10, 2011 at 5:04 | |||||
| Nov 9, 2011 at 12:44 | history | answered | Willie Wong | CC BY-SA 3.0 |