2001
DOI: 10.1590/s0001-37652001000200003
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Abstract: In this note we revisit E. Cartan's address at the 1928 International Congress of Mathematicians at Bologna, Italy. The distributions considered here will be of the same class as those considered by Cartan, a special type which we call strongly or maximally non-holonomic. We set up the groundwork for using Cartan's method of equivalence (a powerful tool for obtaining invariants associated to geometrical objects), to more general non-holonomic distributions.

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Cited by 18 publications
(32 citation statements)
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“…We pursue the (local) classification program proposed by Cartan [1928] using his equivalence method. See Koiller, Rodrigues, and Pitanga [2001] and Tavares [2002] for a rewrite of Cartan's paper in modern language. Cartan's method of equivalence is a powerful method for uncovering and interpreting all differential invariants and symmetries in a given geometric structure.…”
Section: Results On Cartan's Equivalencementioning
confidence: 99%
“…We pursue the (local) classification program proposed by Cartan [1928] using his equivalence method. See Koiller, Rodrigues, and Pitanga [2001] and Tavares [2002] for a rewrite of Cartan's paper in modern language. Cartan's method of equivalence is a powerful method for uncovering and interpreting all differential invariants and symmetries in a given geometric structure.…”
Section: Results On Cartan's Equivalencementioning
confidence: 99%
“…We believe he had in mind the stronger condition for equivalence mentioned above. What was not elucidated by Cartan, or appreciated in [6], is that this strong notion of equivalence is sufficient, but not necessary to maintain the nonholonomic geodesics, as our counterexample in section 4 shows. Proposition 4.1 and theorem 6.1 in [6] are not valid in general for our weak notion of equivalence.…”
mentioning
confidence: 85%
“…What was not elucidated by Cartan, or appreciated in [6], is that this strong notion of equivalence is sufficient, but not necessary to maintain the nonholonomic geodesics, as our counterexample in section 4 shows. Proposition 4.1 and theorem 6.1 in [6] are not valid in general for our weak notion of equivalence. Of course, this minor mistake does not invalidate what is done in that paper -one just has to consider the appropriate stronger notion of equivalence in their statements.…”
mentioning
confidence: 85%
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“…To our knowledge, the only exception is due to Jair Koiller and his colaborators, in a recent preprint that has appeared during the preparation of this work (see [12]), in which they also make a tentative to bring at daylight Cartan's paper. However their methods are very different from those we develop here.…”
Section: Introductionmentioning
confidence: 97%