Timeline for Upper bound on the sectional curvature of the orthogonal group
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2019 at 7:45 | history | edited | Dan Fox | CC BY-SA 4.0 |
added 299 characters in body
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| Oct 9, 2019 at 13:48 | history | edited | Dan Fox | CC BY-SA 4.0 |
added 204 characters in body
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| Oct 8, 2019 at 14:03 | comment | added | Călin | Nevermind, the Lie bracket is already defined for the skew-symmetric part of the tangent vectors, at all points. I'm a novice! | |
| Oct 8, 2019 at 13:45 | comment | added | Călin | Thanks a lot, Dan! Just one follow-up question, to make sure I understand. The last property that you mentioned shows that the sectional curvatures are bounded by $1/4$ at the identity matrix, right? That's because the tangent vectors are like $P = A X$ with $X$ skew-symmetric, so they are generally not skew-symmetric themselves, but if $A = I_n$, they are. And then, to conclude that the inequality holds everywhere, we could invoke the homogeneity of the space. Is that correct? | |
| Oct 8, 2019 at 10:37 | vote | accept | Călin | ||
| Oct 8, 2019 at 10:33 | history | answered | Dan Fox | CC BY-SA 4.0 |