Timeline for Non-flat totally geodesic surfaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2015 at 21:39 | vote | accept | Oliver Jones | ||
| Jul 16, 2015 at 15:58 | history | edited | Robert Bryant |
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| Jul 16, 2015 at 15:57 | answer | added | Robert Bryant | timeline score: 5 | |
| Jul 16, 2015 at 13:37 | comment | added | Robert Bryant | It suffices to consider the irreducible case. Certainly, all the Type II cases will have this property because they are the compact simple Lie groups, and they all contain either a $\mathrm{SO}(3)$ or a $\mathrm{SU}(2)$. Among the Type I cases, i.e., the $G/K$ with $G$ simple and $K$ the fixed subgroup of an involution $\sigma$, the inner ones will have this property ('inner' means $\sigma$ is an inner automorphism). That leaves only A-I, A-II, E-I, and E-IV to check. Now, A-I and A-II have totally geodesic $2$-spheres (by inspection). I'd have to think about E-I and E-IV, but, surely they do. | |
| Jul 15, 2015 at 23:30 | history | asked | Oliver Jones | CC BY-SA 3.0 |