Differential equations and conformal structures
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Cartan, 1921, Sur les espaces conformes generalises et l’universe optique, Comptes Rendus Acad. Sci. Paris, 174, 857
Cartan, 1924, Varietes a connexion projective, Bull. Soc. Math., LII, 205
Cartan, 1941, La geometria de las ecuaciones diferenciales de tercer orden, Rev. Mat. Hispano-Aamer., 4, 1
Cartan, 1910, Les systemes de Pfaff a cinq variables et les equations aux derivees partielles du second ordre, Ann. Sc. Norm. Sup., 27, 109, 10.24033/asens.618
Chern, 1940, The geometry of the differential equations y‴=F(x,y,y′,y″), Sci. Rep. Nat. Tsing Hua Univ., 4, 97
Dunajski, 2001, Einstein–Weyl geometry, the dKP equation and twistor theory, J. Geom. Phys., 37, 63, 10.1016/S0393-0440(00)00033-4
Fefferman, 1976, Monge–Ampere equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. Math., 103, 395, 10.2307/1970945
Fefferman, 1976, Monge–Ampere equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. Math., 104, 393, 10.2307/1970961
Fritelli, 2001, Differential geometry from differential equations, Commun. Math. Phys., 223, 383, 10.1007/s002200100548
Fritelli, 2003, Conformal Lorentzian metrics on the spaces of curves and 2-surfaces, Class. Q. Grav., 20, 3649, 10.1088/0264-9381/20/16/308
A.R Gover, P. Nurowski, Obstructions to conformally Einstein metrics, 2004. math.DG/0405304 at http://xxx.lanl.gov.
Hilbert, 1912, Ueber den Begriff der Klasse von Differentialgleichungen, Mathem. Annalen Bd., 73, 95, 10.1007/BF01456663
M. Godlinski, P. Nurowski, Differential geometry of the third order ODEs, in preparation.
Kobayashi, 1972
Newman, 2003, Projective connections associated with second order ODEs, Class. Q. Grav., 20, 2325, 10.1088/0264-9381/20/11/324
Newman, 1962, An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys., 3, 566, 10.1063/1.1724257
Nurowski, 2003, Three-dimensional Cauchy–Riemann structures and second order ordinary differential equations, Class. Q. Grav., 20, 4995, 10.1088/0264-9381/20/23/004
Olver, 1996
Penrose, 1960, A spinor approach to general relativity, Ann. Phys. (NY), 10, 171, 10.1016/0003-4916(60)90021-X
Petrov, 1954, Classification of spaces defining gravitational fields, Sci. Not. Kazan State Univ., 114, 55
G.A.J. Sparling, Private communications, 2003.
Tod, 2000, Einstein–Weyl spaces and third order differential equations, J. Math. Phys., 41, 5572, 10.1063/1.533426
Wuenschmann, 1905