zbMATH — the first resource for mathematics

Congruence, contact et repères de Frenet. (French) Zbl 0541.53007
Differential geometry, Proc. int. Symp., Peñiscola/Spain 1982, Lect. Notes Math. 1045, 21-35 (1984).
[For the entire collection see Zbl 0517.00006.]
The author analyses the classical notions of congruence relative to a Lie group of transformations as characterized by differential invariants. The main point is a report on a recent Strasbourg thesis of S. Huckel who has derived a satisfactory theorem on the conditions under which the G- contact of a given (computable) order insures the G-congruence. Applications are given to neighborhoods of umbilics on surfaces that escape the classical theorems.
Reviewer: H.Guggenheimer
53A55 Differential invariants (local theory), geometric objects
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces