Timeline for Closed manifolds of nonnegative curvature operator are symmetric spaces
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2021 at 13:40 | vote | accept | C.F.G | ||
| Apr 20, 2021 at 0:23 | answer | added | C.F.G | timeline score: 3 | |
| Apr 19, 2021 at 18:18 | comment | added | Willie Wong | @C.F.G ... hence a comment, just the mention that it is relevant, and not a vote to close as duplicate. | |
| Apr 19, 2021 at 18:00 | comment | added | Igor Belegradek | Yes, I think closed irreductible manifolds of nonnegative curvature operator are diffeomorphic to locally symmetric spaces, see e.g. section 2.4 of arxiv.org/pdf/1511.07899.pdf. | |
| Apr 19, 2021 at 17:53 | comment | added | C.F.G | @IgorBelegradek: I am not sure, but I think so: "all closed manifolds of nonnegative curvature operator are diffeomorphic to locally symmetric spaces?" Someone argued non rigorously like this: a nonnegative curvature operator is of positive curvature operator or its holonomy is not of full rank. Does this help to figure out what is the right statement? | |
| Apr 19, 2021 at 17:47 | comment | added | C.F.G | @WillieWong: my question is different from that linked MO. | |
| Apr 19, 2021 at 17:46 | comment | added | Igor Belegradek | If you slightly deform the standard metric on the unit sphere, you get a metric if positive curvature operator which is not symmetric. The same will happen if you slightly deform a spherical space form. Are you asking if all closed manifolds of nonnegative curvature operator are diffeomorphic to locally symmetric spaces? | |
| Apr 19, 2021 at 16:58 | comment | added | Willie Wong | mathoverflow.net/a/264899/3948 seems relevant. | |
| Apr 19, 2021 at 16:49 | history | asked | C.F.G | CC BY-SA 4.0 |