Abstract
We apply the equivariant method of moving frames to investigate the existence of Poisson structures for geometric curve flows in semi-simple homogeneous spaces. We derive explicit compatibility conditions that ensure that a geometric flow induces a Hamiltonian evolution of the associated differential invariants. Our results are illustrated by several examples of geometric interest.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 532-550 |
| Number of pages | 19 |
| Journal | Regular and Chaotic Dynamics |
| Volume | 15 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2010 |
Bibliographical note
Funding Information:The research of the second author was supported in part by NSF Grant DMS 08-07317.
Keywords
- Poisson structure
- differential invariant
- homogeneous space
- invariant curve flow
- invariant variational bicomplex
- moving frame