Third order ordinary differential equations and Legendre connections
We use N. Tanaka's theory of normal Cartan connections associated with simple graded Lie algebras to study Cartan's equivalence problem of single third order ordinary differential equations under contact transformations. As a result we obtain the complete structure equation with two differential invariants, which is applied on general Legendre Grassmann bundles of three-dimensional contact manifolds.
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 50(4), 993-1013, 1998-10-01
The Mathematical Society of Japan