Differential geometry from differential equations

Communications in Mathematical Physics

Volumn 223, Issue 2, 2001, Pages 383-408

  Frittelli, Simonetta ^a,b   Kozameh, Carlos ^c   Newman, Ezra T ^b  

^a DUQUESNE UNIVERSITY   (United States)

^b UNIVERSITY OF PITTSBURGH   (United States)

^c UNIVERSIDAD NACIONAL DE CÓRDOBA   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035540556     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100548     Document Type: Article

References (15)

1. 1. Cartan, E.: Les Espaces Generalises e L'integration de Certaines Classes d'Equations Differentielles. C. R. Acad. Sci. 206, 1425-1429 (1938).
2. 2. Cartan, E.: La Geometria de las Ecuaciones Diferenciales de Tercer Orden. Rev. Mat. Hispano-Amer. 4, 1-31 (1941)
3. 3. Cartan, E.: Sur une Classe d'Espaces de Weyl. Ann. Sc. Ec. Norm. Sup. 3e serie 60, 1-16 (1943)
4. 4. Chern, S.-S.: The Geometry of the Differential Equation y‴ = F(x, y, y′, y″). In Selected Papers. Berlin-Heidelberg-New York; Springer-Verlag, 1978 (original 1940)
5. 5. Wunschmann, K.: Über Berührungsbedingungen bei Integralkurven von Differentialgleichungen. Inaug. Dissert., Leipzig: Teubner
6. 6. Tod, K.P.: Einstein-Weyl Spaces and Third Order Differential Equations, J. Math. Phys. 41, 5572 (2000)
7. 7. Bryant, R.L.: Proc. Symp. Pure. Maths. Vol. 53, 33-88 (1991)
8. 8. Though there is a simple heuristic argument for the four-dimensionality of the solution space, recently, in a private communication, Peter Vassiliou and Niky Kamran have given a rigorous proof of this.
9. 9. Frittelli, S., Kozameh, C., Newman, E.: GR Via Characteristic Surfaces. J. Math. Phys. 36, 4984 (1995)
10. 10. Frittelli, S., Kozameh, C., Newman, E.: Lorentzian Metrics from Characteristic Surfaces. J. Math. Phys. 36, 4975 (1995)
11. 11. Frittelli, S., Kozameh, C., Newman, E.: Dynamics of Light cone Cuts of Null Infinity. Phys. Rev. D 56, 4729 (1997)
12. 12. Frittelli, S., Kozameh, C., Newman, E.: Linearized Einstein Theory Via Null Surfaces. J. Math. Phys. 36, 5005 (1995)
13. 13. Forni, D., Iriondo, M., Kozameh, C.: Null Surface Formulation in 3D. J. Math. Phys. 41, 5517 (2000)
14. 14. Tanimoto, M.: On the Null Surface Formalism, gr-qc/9703003 (1997)
15. 15. Frittelli, S., Kamran, N., Newman, E.: Differential Equations and Conformal Geometry. Preprint (2001)