Einstein-Weyl spaces and third-order differential equations

Journal of Mathematical Physics

Volumn 41, Issue 8, 2000, Pages 5572-5581

  Tod, K P ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034336595     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533426     Document Type: Article

References (16)

1. S. Frittelli, C. N. Kozameh, and E. T. Newman, "Lorentzian metrics from characteristic surfaces," J. Math. Phys. 36, 4975-4983 (1995).
2. S. Frittelli, C. N. Kozameh, and E. T. Newman, "GR via characteristic surfaces," J. Math. Phys. 36, 4984-5005 (1995).
3. S. Frittelli, C. N. Kozameh, and E. T. Newman, "Linearized Einstein theory via null surfaces," J. Math. Phys. 36, 5005-5022 (1995).
4. E. T. Newman, "Heaven and its properties," Gen. Rel. Grav. 7, 107-111 (1976).
5. R. O. Hansen, E. T. Newman, R. Penrose, and K. P. Tod, "The metric and curvature properties of H-space," Proc. R. Soc. London, Ser. A 463, 445-468 (1978).
6. M. Tanimoto, "On the null surface formalism," Report No. gr-qc/9703003 (1997).
7. D. M. Forni, M. Iriondo, and C. N. Kozameh, "Null surfaces formulation in 3D," J. Math. Phys. (to be published).
8. N. J. Hitchin, "Complex manifolds and Einstein's equations," in Twistor geometry and non-linear systems, edited by H. D. Doebner and T. D. Palev, Springer Lecture Notes in Mathematics, 1982, Vol. 970.
9. P. E. Jones and K. P. Tod, "Minitwistor spaces and Einstein-Weyl spaces," Class. Quantum Grav. 2, 565-577 (1985).
10. H. Pedersen and K. P. Tod, "Three-dimensional Einstein-Weyl geometry," Adv. Math. 97, 74-109 (1993).
11. E. Cartan, "Les espaces généralisées et l'intégration de certaines classes d'équations différentielles," C.R. Acad. Sci. 206, 1425-1429 (1938).
12. E. Cartan, "La geometria de las ecuaciones diferenciales de tercer orden," Rev. Mat. Hispano-Amer. 4, 1-31 (1941).
13. E. Cartan, "Sur une classe d'espaces de Weyl," Ann. Sc. Ec. Norm. Sup. 3e série 60, 1-16 (1943).
14. K. Wünschmann, "Ueber Berührungsbedingungen bei Integralkurven von Differentialgleichungen," Inaugural Dissertation, Teubner, Leipzig.
15. S-S. Chern, "The geometry of the differential equation y‴ = F(x,y,y′,y″)," [13] in Selected Papers (Springer-Verlag, Berlin, 1978).
16. 6W. P. Thurston, "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry," AMS. Proc. Symp. Pure Math. 39, 87-111 (1983).