Timeline for The midpoint geodesic
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2016 at 13:11 | comment | added | Willie Wong | One thing to try is to take a warped product of what I outlined above with a copy of $\mathbb{H}^2$; this way the geodesics orthogonal to the $\mathbb{H}^2$ factor remains unchanged. To ensure constant scalar curvature you will have to solve an second order ODE in $r$ for the warping factor; if this ODE can be solved to have a global positive solution you will get an example. There's a one parameter freedom in choosing the constant for the scalar curvature, perhaps the ODE only has a good ground state for a good choice of this constant. | |
| Sep 27, 2016 at 13:02 | comment | added | Willie Wong | In two dimensions the answer is trivial if you make the scalar curvature constant. Generally as dimension increase, scalar curvature becomes weaker and weaker as restriction on geometry, so if you ask me to bet I would say that for sufficiently high dimensions there may be counterexamples. I don't have a proof one way or another. | |
| Sep 27, 2016 at 10:25 | comment | added | Giulio | @what about if the scalar curvature is constant? Thanks | |
| Aug 2, 2016 at 17:32 | vote | accept | Giulio | ||
| Jul 29, 2016 at 15:57 | history | edited | Willie Wong | CC BY-SA 3.0 |
added 99 characters in body
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| Jul 29, 2016 at 15:43 | history | answered | Willie Wong | CC BY-SA 3.0 |