Timeline for When is a Divergence-Free Vector Field on the Tangent Bundle of a Riemannian Manifold Hamiltonian?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2018 at 4:13 | comment | added | Jeffrey Rolland | One trip to the library later: $DX$ is the Jacobian matrix and the matrix A is $\Omega$-skew iff $\Omega(Au,v) = -\Omega(u,Av)$ for all $u,v \in Z$; thanks so much for all your help. | |
| Jan 4, 2018 at 17:05 | comment | added | Jeffrey Rolland | Nawaf Bou-Rabee: Wonderful addition! That's very helpful. | |
| Jan 4, 2018 at 16:33 | comment | added | Nawaf Bou-Rabee | To be sure, the additional structure of a Riemannian metric is not necessary to determine whether a given vector field is Hamiltonian or not. | |
| Jan 4, 2018 at 16:29 | comment | added | Jeffrey Rolland | Thanks! I'll have to look at the book (I'm not sure what $DX$ [induced map on double-tangent bundle?] and $\Omega$-skew mean in this context), but I think that's for what I'm looking. (I love Marsden as an author.) | |
| Jan 4, 2018 at 16:20 | history | answered | Nawaf Bou-Rabee | CC BY-SA 3.0 |