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ISSN 1088-6850(e) ISSN 0002-9947(p)

Pfaffian systems with derived length one. The class of flag systems

Author(s): María A. Cañadas-Pinedo; Ceferino Ruiz
Journal: Trans. Amer. Math. Soc. 353 (2001), 1755-1766.
MSC (2000): Primary 58A17, Scondary, 53C10
Posted: January 16, 2001
MathSciNet review: 1813594
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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.

References:

1.: R. BRYANT, S. S. CHERN, R. B. GARDNER, H. GOLDSCHMIDT & P. A. GRIFFITHS, Exterior Differential Systems, MSRI Pub., 18, Springer-Verlag, New York (1991). MR 92h:58007
2.: M. A. CA $\tilde{\mbox{N}}$ ADAS-PINEDO & C. RUIZ, Differential Invariants of Pfaffian Systems. Equivalence in dimension five, Anales de Física, Monografías, 3 (1996), 71-81. MR 97m:58005
3.: M. A. CA $\tilde{\mbox{N}}$ ADAS-PINEDO & C. RUIZ, Sternberg's structure function of differential systems in dimension five, Czechoslovak Math. J., 43 (1993), 429-438. MR 94k:58005
4.: É. 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.
5.: R. B. GARDNER, Invariants of Pfaffian systems, Trans. Amer. Math. Soc., 126 (1967), 514-533. MR 35:2233
6.: R. B. GARDNER & N. KAMRAN, Normal Forms and Focal Systems for Determined Systems of Two First-Order Partial Differential Equations in the Plane, Indiana Univ. Math. J., 44 (1995), 1127-1162. MR 97i:58006
7.: M. GASPAR, A. KUMPERA & C. RUIZ, Sur les systèmes de Pfaff en Drapeau, An. Acad. Brasil. Ciênc., 55 (1983), 225-230. MR 85e:58001
8.: A. KUMPERA & C. RUIZ, Sur l'équivalence locale des Systèmes de Pfaff en Drapeau, Ist. Naz. Alta Mat. Francesco Severi, Rome, 1982. MR 84k:58011
9.: P. J. OLVER, Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Math., 107, Springer-Verlag, New York (1993). MR 94g:58260
10.: S. STERNBERG, Lectures on Differential Geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1964). MR 33:1797
11.: K. YANG, Exterior Differential Systems and Equivalence Problems, Mathematics and its Applications, Kluwer Academic Pub., Dordrecht (1992). MR 93m:58005

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Additional Information:

María A. Cañadas-Pinedo
Affiliation: Departamento Álgebra, Geometría y Topología, Fac. Ciencias, Universidad de Málaga, Campus de Teatinos, Apdo. 59, 29080 - Málaga, Spain
Email: pinedo@uma.es

Ceferino Ruiz
Affiliation: Departamento Geometría y Topología, Universidad de Granada, 18071 - Granada, Spain
Email: ruiz@ugr.es

DOI: 10.1090/S0002-9947-01-02638-1
PII: S 0002-9947(01)02638-1
Keywords: Pfaffian systems, structure tensor, characteristic system, derived system, flag systems.
Received by editor(s): August 3, 1999
Received by editor(s) in revised form: October 1, 1999
Posted: January 16, 2001
Additional Notes: Research partially supported by a DGICYT grant PB94-0796
Copyright of article: Copyright 2001, American Mathematical Society

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