Third order ordinary differential equations and Legendre connections
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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.
- Tokyo Sugaku Kaisya Zasshi
Tokyo Sugaku Kaisya Zasshi 50(4), 993-1013, 1998-10-01
The Mathematical Society of Japan