Sternberg’s structure function of differential systems in dimension five. (English) Zbl 0804.53040

The authors present explicit calculations (reduction algorithms without prolongation) to the equivalence problem of general Pfaffian systems of constant rank 3 in a 5-dimensional space (completely discussed by Cartan in his famous paper dated 1910). The corresponding first-order \(G\)- structure designed \(G_{19}\) (of fiber dimension 19) is reduced to \(G_{16}\), and then to \(G_{12}\), by using the first-order Sternberg’s structure function. The paper is an instructive complement to the mentioned Cartan’s paper.
Reviewer: J.Chrastina (Brno)


53C10 \(G\)-structures
58A17 Pfaffian systems
Full Text: EuDML


[1] E. Cartan: Les systèmes de Pfaff à cinq variables at les équations aux dérivées partielles du seconde ordre. Ann. Sc. Normale Sup. 27 (1910), 109-192. · JFM 41.0417.01
[2] S. Sternberg: Lectures on differential geometry. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964;. · Zbl 0129.13102
[3] R. B. Gardner: The method of equivalence and its applications. CBMS-NFS regional conference series in applied mathematics, 58, S.I.A.M. Philadelphia, Pennsylvania, 1989. · Zbl 0694.53027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.