Timeline for Warped product neighborhoods of geodesic hypersurfaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2011 at 8:32 | answer | added | Chih-Wei Chen | timeline score: 2 | |
| Aug 19, 2011 at 10:30 | comment | added | Anton Petrunin | Assume "yes" for a hypesurface $\Sigma$. Then you have to have warped product of $\Sigma$ with an interval. The horizontal lines have to be geodesics perpendicular to $\Sigma$. Then easy calculations show that all principle curvatures of $\Sigma$ have to be the same. So $\Sigma$ is (a domain in) a hyperplane or round sphere. | |
| Aug 17, 2011 at 15:59 | comment | added | Deane Yang | If you google "warped product", you can find a nice set of notes by Peter Petersen of UCLA. I agree with Jean-Marc that it seems unlikely to be true. Why do you think it might be? | |
| Aug 17, 2011 at 14:40 | comment | added | Jean-Marc Schlenker | I don't think so -- you need some additional hypothesis on the manifold, for instance constant curvature? Or low dimension? | |
| Aug 17, 2011 at 13:13 | history | asked | anonymous | CC BY-SA 3.0 |