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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {V. S. Dryuma},
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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/

[1] V. Dryuma, Buletinul AS RM (mathematica), Kishinev, 3:31 (1999), 95–102 | MR | Zbl

[2] V. Dryuma, Mathematical Researches (Kishinev), 112 (1990), 93–103 | MR | Zbl

[3] V. S. Dryuma, “On initial values problem in theory of the second order ODE's”, Proc. Workshop on Nonlinearity, Integrability, and All That: Twenty years after NEEDS'79 (Gallipoli (Lecce), Italy, July 1–July 10, 1999), eds. M. Boiti, L. Martina, F. Pempinelli, B. Prinari, G. Soliani, World Scientific, Singapore, 2000, 109–116 | DOI | MR | Zbl

[4] V. S. Dryuma, “O geometrii differentsialnykh uravnenii vtorogo poryadka”, Trudy vsesoyuznoi konferentsii “Nelineinye uravneniya”, ed. K. V. Frolov, Nauka, M., 1991, 41–48

[5] V. S. Dryuma, TMF, 99 (1994), 241–249 | MR | Zbl

[6] V. S. Dryuma, “Geometrical properties of nonlinear dynamical systems”, Proc. First Workshop on Nonlinear Physics (Le Sirenuse, Gallipoli (Lecce), Italy, June 29–July 7, 1995), eds. E. Alfinito, M. Boiti, L. Martina, F. Pempinelli, World Scientific, Singapore, 1996, 83–93 | MR | Zbl

[7] R. Liouville, J. École Polytec., 59 (1889), 7–76

[8] A. Tresse, Détermination des Invariants Ponctuels de l'Équation Differentielle Ordinaire de Second Ordre: $y''=w(x,y,y')$, Preisschriften der fürstlichen Jablonowski'schen Gesellschaft, 32, S. Hirzel, Leipzig, 1896

[9] A. Tresse, Acta Math., 18 (1894), 1–88 | DOI | MR

[10] E. Cartan, Bull. Soc. Math. France, 52 (1924), 205–241 | DOI | MR | Zbl

[11] E. M. Paterson, A. G. Walker, Quart. J. Math. Oxford, 3 (1952), 19–28 | DOI | MR

[12] E. Wilczynski, Trans. Am. Math. Soc., 9 (1908), 103–128 | MR

[13] E. Cartan, Ann. Sci. École Normale Sup., 14 (1943), 1–16 | DOI | MR

[14] H. Pedersen, K. P. Tod, Adv. Math., 97 (1993), 71–109 | DOI | MR

[15] J. Chazy, C. R. Acad. Sci. Paris, 150 (1910), 456–458 | Zbl

[16] R. Ward, Class. Q Grav., 7 (1980), L45–L48

[17] M. Dunaisjski, L. Mason, P. Tod, Einstein–Weyl geometry, the dKP equation, and twistor theory, E-print math.DG/0004031 | MR