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

Denis Serre
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asked Jul 23 2011 at 14:31

jim stasheff
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	I don't understand the question. What does "structure determined by a 3rd order partial" mean? – Hans Stricker Jul 23 2011 at 14:49
	Have you considered having a look at math.stackexchange.com/questions/14841 ? Or else, to repeat the question of Hans: what is your question? – András Bátkai Jul 23 2011 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 2011 at 19:56

Denis Serre · Answer 1 · 2011-07-23 14:47:01Z UTC

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

answered Jul 23 2011 at 14:47

Denis Serre
18.7k●1●31●93

José Figueroa-O'Farrill · Answer 2 · 2011-07-24 11:35:09Z UTC

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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 2011 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 2011 at 11:48
	Jim, glad to have been of help! – José Figueroa-O'Farrill Jul 25 2011 at 12:00

higher order structure by higher order derivatives