## 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)

### MSC:

 53C10 $$G$$-structures 58A17 Pfaffian systems
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### References:

 [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
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