Differential equations and conformal structures

Journal of Geometry and Physics - Tập 55 Số 1 - Trang 19-49 - 2005
Paweł Nurowski1
1Uniwersytet Warszawski - Wydział Fizyki - Instytut Fizyki Teoretycznej - Katedra Teorii Względności i Grawitacji

Tóm tắt

Từ khóa


Tài liệu tham khảo

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, 1995, GR via characteristic surfaces, J. Math. Phys., 36, 4984, 10.1063/1.531210

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

Penrose, 1967, Twistor algebra, J. Math. Phys., 8, 345, 10.1063/1.1705200

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