Abstract
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 inv riants, which is applied on general Legendre Grassmann bundles of three-dimensional contact manifolds.
Citation
Hajime SATO. Atsuko Yamada YOSHIKAWA. "Third order ordinary differential equations and Legendre connections." J. Math. Soc. Japan 50 (4) 993 - 1013, October, 1998. https://doi.org/10.2969/jmsj/05040993
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