In his work on projective connections, Cartan discusses his theory of second order differential equations. It is the aim here to look at how a normal projective connection can be constructed and how it relates to the geometry of a single second order differential equation. The calculations are presented in some detail in order to highlight the use of gauge conditions
Bracken, P. (2020). Cartan's Approach to Second Order Ordinary Differential Equations. European Journal of Pure and Applied Mathematics, 13(4), 1016-1034. doi:https://doi.org/10.29020/nybg.ejpam.v13i4.3868
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European Journal of Pure and Applied