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.
Bibliographical noteFunding Information:
The research of the second author was supported in part by NSF Grant DMS 08-07317.
- Poisson structure
- differential invariant
- homogeneous space
- invariant curve flow
- invariant variational bicomplex
- moving frame