1. CJM 2016 (vol 68 pp. 445)
||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.
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