References
- Anco , S . 2006 . Bi-Hamiltonian operators, integrable flows of curves using moving frames, and geometric map equations . J. Phys. A: Math. Gen. , 39 : 2043 – 2072 .
- Chou , K-S and Qu , C . 2002 . Integrable equations arising from motions of plane curves . Phys. D , 162 : 9 – 33 .
- Chou , K-S and Qu , C . 2003 . Integrable equations arising from motions of plane curves II . J. Nonlinear Sci. , 13 : 487 – 517 .
- Marí Beffa , G . 2006 . Poisson geometry of differential invariants of curves in some nonsemisimple homogenous spaces . Proc. Amer. Math. Soc. , 134 : 779 – 791 .
- Marí Beffa , G . On bi-Hamiltonian flows and their realizations as curves in real semisimple homogeneous manifolds . Available at http://www.math.wisc.edu/maribeff
- Marí Beffa , G , Sanders , JA and Wang , JP . 2002 . Integrable systems in three-dimensional Riemannian geometry . J. Nonlinear Sci. , 12 : 143 – 167 .
- Sanders , J and Wang , JP . 2004 . Integrable systems in n-dimensional Riemannian geometry . Moscow Math. J. , 3
- Terng , CL and Uhlenbeck , K . 2006 . “ Schrödinger flows on Grassmannians, Integrable systems, geometry and topology ” . In AMS/IP Stud. Adv. Math , 235 – 256 . Providence : AMS .
- Hasimoto , R . 1972 . A soliton on a vortex filament . J. Fluid Mechanics , 51 : 477 – 485 .
- Squires , S and Stephenson , G . 2006 . Differential invariants of curves in flat Galilean and Minkowski manifolds, a report submitted to the NSF VIGRE Grant for UW-Madison .
- Ivey , T . 2001 . Integrable geometric evolution equations for curves . Contemp. Math. , 285 : 71 – 84 .
- Fels , M and Olver , PJ . 1998 . Moving coframes. I. A practical algorithm . Acta Appl. Math. , 51 ( 2 ) : 99 – 136 .
- Fels , M and Olver , PJ . 1999 . Moving coframes. II. Regularization and theoretical foundations . Acta Appl. Math. , 55 ( 2 ) : 127 – 208 .
- Green , ML . 1978 . The moving frame, differential invariants and rigidity theorems for curves in homogeneous spaces . Duke Math. J. , 45 : 735 – 779 .
- Sharpe , RW . 1997 . Differential Geometry: Cartan's Generalization of Klein's Erlangen Program , New York : Springer-Verlag .
- Olver , PJ . 1995 . Equivalence, Invariance and Symmetry , Cambridge : Cambridge University Press .
- Magri , F . 1978 . A simple model of the integrable Hamiltonian equation . J. Math. Phys. , 19 : 1156 – 1162 .
- Olver , PJ . 1986 . Applications of Lie Groups to Differential Equations , New York : Springer-Verlag .