Pfaffian Systems' Characterizations. Consequences in Dimension Five
by
María A. Cañadas-Pinedo
Universidad de Málaga, Spain
Coauthors: C. Ruiz (Universidad de Granada)

Oral Communication

The aim of this talk is to obtain which Élie Cartan calls Première classification des systèmes de deux ou trois équations de Pfaff à cinq variables (see [C]). The main newness is that we obtain such classification in an intrinsic way, and not by using coordinates, as it was traditional in works concerning to Pfaffian systems.

The technique we use is based in the study of the incidence relations between a Pfaffian system and the characteristic of its first derived system. More details can be found in [CP-R;2]. By using this technique, that we develope in [CP-R;3], we obtain several classifications results for Pfaffian systems. In particular we characterize Pfaffian systems with derived lenght one, that is, Pfaffian systems whose first derived system is an integrable system, and we also give a characterization for flag systems in terms of the class.

Those results are used to obtain the whole classification of Pfaffian systems up to dimension four and the first classification in dimension five in an intrinsic way (see[CP-R;4]). Related results concerning dimension five can be found in [CP-R;1].

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. A. CAÑADAS-PINEDO & C. RUIZ, Sternberg's structure function of differential systems in dimension five, Czechoslovak Math. J., 43 (1993), 429-438.

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.A. CAÑADAS-PINEDO & C. RUIZ, Incidence relations between a Pfaffian system and the characteristic of its first derived system, Proceedings del Encuentro de Otoño de Geometría y Aplicaciones, Valencia, (1998) (to appear)

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. A. CAÑADAS-PINEDO & C. RUIZ , Pfaffian Systems with Derived Length One. The Class of Flag Systems, Trans. Amer. Math. Soc. (to appear )

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. A. CAÑADAS-PINEDO & C. RUIZ , First Classification of Pfaffian Systems in Dimension Five, Preprint, (2000).

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E. CARTAN, Les systèmes de Pfaff à cinq variables et les équations aux dérivées partielles du seconde ordre, Ann. Sc. Normale Sup., 27 (1910), 109-192.

Date received: May 30, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-94.