1. CJM Online first
|Geometric invariants of cuspidal edges|
We give a normal form of the cuspidal edge which uses only diffeomorphisms on the source and isometries on the target. Using this normal form, we study differential geometric invariants of cuspidal edges which determine them up to order three. We also clarify relations between these invariants.
Keywords:cuspidal edge, curvature, wave fronts
Categories:57R45, 53A05, 53A55
2. CJM 2003 (vol 55 pp. 266)
|Two Algorithms for a Moving Frame Construction |
The method of moving frames, introduced by Elie Cartan, is a powerful tool for the solution of various equivalence problems. The practical implementation of Cartan's method, however, remains challenging, despite its later significant development and generalization. This paper presents two new variations on the Fels and Olver algorithm, which under some conditions on the group action, simplify a moving frame construction. In addition, the first algorithm leads to a better understanding of invariant differential forms on the jet bundles, while the second expresses the differential invariants for the entire group in terms of the differential invariants of its subgroup.
Categories:53A55, 58D19, 68U10