Timeline for SO(3) action on (simply connected) 6 manifold with discrete fixed point
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2017 at 14:02 | comment | added | Yuhang Liu | Yes. Taking product preserves positive Ricci curvature but not positive sectional curvature. $S^3\times S^3$ would also be an example. It seems somehow Fang could rule out those product manifolds(assuming SU(2) or SO(3) symmetry), leaving $S^2\times S^4$ as a possible exception. However I don't quite understand his arguments.. | |
| Apr 14, 2017 at 19:59 | comment | added | Nick L | I would add that this action preseves a metric with positive definite Ricci curvature (Since $S^{2} \times S^{2} \times S^{2}$ is a Fano 3-fold), which is still weaker than what you ask. | |
| Apr 14, 2017 at 18:14 | comment | added | Nick L | Ahh this is more subtle than I thought. I do not know the answer to your question. | |
| Apr 14, 2017 at 18:09 | comment | added | Yuhang Liu | Does S^2*S^2*S^2 admit positive sectional curvature? That's basically the Hopf conjecture.. Positivity of curvature puts strong restriction on topology. | |
| Apr 14, 2017 at 15:56 | history | answered | Nick L | CC BY-SA 3.0 |