Timeline for Infinitesimal rigidity vs local rigidity of isometrically immersed riemannian manifolds
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2021 at 23:33 | comment | added | Deane Yang | Yes, it's a straightforward argument. | |
| Jan 11, 2021 at 23:29 | comment | added | Mircea | @DeaneYang thanks, probably this paper is a good place to start in the above. You think that the generalization to $W^{2,2}$ is doable by classical techniques? | |
| Jan 11, 2021 at 16:21 | history | edited | Mircea | CC BY-SA 4.0 |
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| Jan 11, 2021 at 15:49 | comment | added | Mircea | @MoisheKohan true, I was superficial in my relation of the above statement, I will correct it. | |
| Jan 10, 2021 at 23:10 | comment | added | Moishe Kohan | I did not read the cited paper but the claimed result that local rigidity for frameworks is equivalent to infinitesimal rigidity is simply false. What's true is that infinitesimal rigidity for frameworks implies local rigidity. | |
| Jan 10, 2021 at 22:42 | comment | added | Deane Yang | I believe that your question is wide open. I do, however, want to call attention to the work of Berger-Bryant-Griffiths (projecteuclid.org/euclid.dmj/1077303336), who prove rigidity results by studying when the Gauss, Codazzi, and Ricci equations have unique solutions pointwise solutions. In particular, the rigidity theorem they prove where curvature tensor uniquely determines the second fundamental form can be generalized to situations where the Riemannian metric is at least $C^2$ and the isometric embedding is assumed to be only $W^{2,2}$. | |
| Jan 10, 2021 at 17:01 | history | asked | Mircea | CC BY-SA 4.0 |