Abstract. The incidence relations between a Pfaffian system and the characteristic system of its first derived system lead to obtain a characterization of Pfaffian systems with derived length one. Also, for flag systems, several properties are studied. In particular, an intrinsic proof of a result which determines the class of a system and of all the derived systems is given.
We obtain in this work, in an intrinsic way, the First classification of Pfaffian systems of rank two and three in dimension five, as well as a complete classification up to dimension four. For the general case, we prove that there exists a one-to-one correspondence, which is explicitly given, between Pfaffian systems of rank two and Pfaffian systems of rank three. That is, for a Pfaffian system of rank two in dimension five, the covariant system is constructed.
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