higher order structure by higher order derivatives

Question

Anyone recall a structure determined by a 3rd order partial derivative? not the general nth order of recent Baranovsky

I don't understand the question. What does "structure determined by a 3rd order partial" mean? — Hans-Peter Stricker, Jul 23 '11 at 14:49
Have you considered having a look at http://math.stackexchange.com/questions/14841 ? Or else, to repeat the question of Hans: what is your question? — András Bátkai, Jul 23 '11 at 19:33
Just in case (but I am to far from this topic): a foliated $3$-web in the plane is linearizable if and only if its curvature is $\equiv0$. Isn't true that this curvature involves the third derivatives of the vector field defining the foliations ? — Denis Serre, Jul 23 '11 at 19:56

score 6 · Answer 1 · answered Jul 23 '11 at 14:47

6

The Schwarzian derivative is third-order and plays an important role in the geometry of the projective line.

answered Jul 23 '11 at 14:47

Denis Serre

score 4 · Answer 2 · answered Jul 24 '11 at 11:35

4

The associativity condition for the symmetric 3-tensor in a Frobenius manifold is a third-order PDE on the potential: the so-called WDVV equation.

answered Jul 24 '11 at 11:35

Jos'e, That is the one I was after. Apologies for the vagueness of my question,thinking it did have something to do with Frobenius manifolds, but having not found the answer in Dubrovin, I thought that too might be a faulty memory. – Jim Stasheff Jul 25 '11 at 11:48
Jim, glad to have been of help! – José Figueroa-O'Farrill Jul 25 '11 at 12:00

2 Answers2