Geodesic
Applications of Riemannian and Einstein–Weyl Geometry in the Theory of Second-Order Ordinary Differential Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 1, pp. 15-26 
V. S. Dryuma. Applications of Riemannian and Einstein–Weyl Geometry in the Theory of Second-Order Ordinary Differential Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 1, pp. 15-26. http://geodesic.mathdoc.fr/item/TMF_2001_128_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider some properties of four-dimensional Riemannian spaces whose metric coefficients are associated with the coefficients of second-order nonlinear differential equations, and we study the properties of three-dimensional Einstein–Weyl spaces related to the dual equations $b''=g(a,b,b')$, where the function $g(a,b,b')$ satisfies a special partial differential equation.

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