MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Hello everybody, I would like to know about the work of Élie Cartan of PDE's that relate to the theory of foliations and differential forms.

I am interested in the subject and will be happy to receive basic references on the subject (articles) as well as explanations on the importance of the subject in mathematics today.

share|cite|improve this question
I'm wondering if this question is a bit overbroad. (See the FAQ.) Also I am not sure why the OP wanted a dynamical-systems tag on this question. For the time being I'll leave it there. – Willie Wong Aug 27 '10 at 16:01
A starting point may be section 2 of – Willie Wong Aug 27 '10 at 16:05
I was going to suggest the book by Bryant, Chern, ... on Exterior Differential Systems, which is available for free from the MSRI:… – José Figueroa-O'Farrill Aug 27 '10 at 16:13
Ivey and Landsberg, cartan for beginners – Deane Yang Aug 27 '10 at 16:46
Thanks Wong, Yang and Figueroa! It is a good start for my bibliographic research – Klein Aug 27 '10 at 18:43
up vote 13 down vote accepted

Robert Bryant is the reigning expert on this. An excellent book on the subject (later than the one mentioned) is: Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics (2003), University of Chicago Press (vii+213 pages, ISBN: 0-226-07794-2.) by R. Bryant, Phillip Griffiths and Dan Grossmann.

I just recalled, Bryant has a very nice set of nine introductory lectures on the subject. It may be just what you are looking for! They are available online here:

share|cite|improve this answer
A preliminary version of the book is available on the arXiv: – Willie Wong Aug 27 '10 at 22:05
thanks Palais and Wong! – Klein Aug 28 '10 at 1:48
Hi, I made the address of the nine lectures a genuine link. Will. – Will Jagy Aug 28 '10 at 4:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.