A class of Einstein-Weyl spaces associated to an integrable system of hydrodynamic type

Journal of Geometry and Physics

Volumn 51, Issue 1, 2004, Pages 126-137

  Dunajski, Maciej ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Einstein Weyl geometry; Integrable systems; Twistor theory

Indexed keywords

EID: 1842502039     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2004.01.004     Document Type: Article

References (23)

1. Calderbank D.M.J. Pedersen H. Self-dual spaces with complex structures, Einstein-Weyl geometry and geodesics Ann. Inst. Fourier (Grenoble) 503 2000 921-963
2. Cartan E. Sur une classe d'espaces de Weyl Ann. Sci. Ecole Norm. Suppl. 60 1943 1-16
3. Dunajski, M. The nonlinear graviton as an integrable system, D.Phil. Thesis, Mathematical Institute, Oxford, 1998.
4. Dunajski M. The twisted photon associated to hyper-Hermitian four manifolds J. Geom. Phys. 30 1999 266-281
5. Dunajski M. Mason L.J. Tod K.P. Einstein-Weyl geometry, the dKP equation and twistor theory J. Geom. Phys. 37 2001 63-92
6. Dunajski M. Tod K.P. Einstein-Weyl structures from hyper-kähler metrics with conformal Killing vectors Diff. Geom. Appl. 14 2001 39-55
7. Ferapontov E.V. Korotkin D.A. Shramchenko V.A. Boyer-Finley equation and systems of hydrodynamic type Class. Quant. Grav. 19 2002 L1-L6
8. Ferapontov E.V. Pavlov M.P. Hydrodynamic reductions of the heavenly equation Class. Quant. Grav. 20 2003 1-13
9. Ferapontov, E.V. Khusnutdinova, K.R. On the integrability of (2+1)-dimensional quasilinear systems, Commun. Math. Phys., in press. nlin.SI/0305044.
10. Ferapontov, E.V. Khusnutdinova, K.R. The characterisation of two-component (2+1)-dimensional quasilinear systems, 2003. nlin.SI/0310021.
11. Gauduchon P. Tod K.P. Hyper-Hermitian metrics with symmetry J. Geom. Phys. 25 1998 291-304
12. Gibbons J. Tsarev S.P. Reductions of the Benney equations Phys. Lett. A 211 1996 19-24
13. Hitchin, N. Complex manifolds and Einstein's equations, in: H.D. Doebner, T.D. Palev (Eds.), Twistor Geometry and Non-linear Systems, Springer Lecture Notes in Mathematics, vol. 970, 1982.
14. Jones P. Tod K.P. Minitwistor spaces and Einstein-Weyl spaces Class. Quant. Grav. 2 1985 565-577
15. Konopelchenko B.G. Martinez Alonso L. Ragnisco O. The ∂̄-approach to the dispersionless KP hierarchy J. Phys. A 3447 2001 10209-10217
16. Krichever I.M. The τ-function of the universal Whitham hierarchy, matrix models and topological field theories Commun. Pure Appl. Math. 474 1994 437-475
17. Martinez Alonso L. Shabat A.B. Towards a theory of differential constraints of a hydrodynamic hierarchy J. Nonlinear Math. Phys. 102 2003 229-242
18. Pavlov, M.V. Integrable hydrodynamic chains, J. Math. Phys. 44 (9) (2003).
19. Pedersen H. Tod K.P. Three-dimensional Einstein-Weyl geometry Adv. Math. 97 1993 74-109
20. Plebański J.F. Some solutions of complex Einstein equations J. Math. Phys. 16 1975 2395-2402
21. Takasaki K. Takebe T. Integrable hierarchies and dispersionless limit Rev. Math. Phys. 7 1995 743-808
22. Tsarev S.P. Geometry of Hamiltonian systems of hydrodynamic type. Generalized hodograph method Izv. AN USSR Math. 545 1990 1048-1068
23. Zakharov, E.V. Dispersionless limit of integrable systems in 2+1 dimensions, in: N.M. Ercolani, et al. (Eds.), Singular Limits of Dispersive Waves, Plenum Press, New York, 1994, pp. 165-174.