Moving frames method
The equivalence moving frames method was introduced by E. Cartan to solve the equivalence problems on submanifolds under the action of a transformation group. In 1974, P. A. Griffiths has paid to the uniqueness and existence problem on geometric differential equations by using the Cartan method of Lie groups and moving frames [1]. Later on, in the 1990s, Fels and Olver have presented the moving co-frame method as a new formulation of the classical Cartan method for finite-dimensional Lie group actions on manifolds [2][3]. In the last two decades, the moving frames method has been developed in the general algorithmic and equivariant framework which gives several new powerful tools for finding and classifying the equivalence and symmetry properties of submanifolds, differential invariants, and their syzygies.
- ^ Griffiths, P. A. (1974). "On Cartan's method of Lie groups and moving frames as applied to uniqueness
and existence questions in differential geometry". Duke Math. J. 41: 775–814.
{{cite journal}}: line feed character in|title=at position 76 (help) - ^ M. Fels and P. J. Olver (1998). "Moving coframes-I: A practical algorithm". Acta Appl. Math. 51: 161–213.
- ^ M. Fels and P. J. Olver, (1999). "Moving coframes-II: Regularization and theoretical foundations". Acta Appl. Math. 55 (2): 127–208.
{{cite journal}}: line feed character in|journal=at position 5 (help)CS1 maint: extra punctuation (link)