Hyper-Kähler hierarchies and their twistor theory

Communications in Mathematical Physics

Volumn 213, Issue 3, 2000, Pages 641-672

  Dunajski, Maciej ^a   Mason, Lionel J ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349419     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005532     Document Type: Article

References (32)

1. 1. Ablowitz, M.J., Clarkson, P.A.: Solitons, Nonlinear evolution equations and inverse scattering. L.M.S. Lecture note series, 149. Cambridge: CUP, 1992
2. 2. Bailey, T.N., Eastwood, M.G.: Complex paraconformal manifolds - their differential geometry and twistor theory. Forum Math. 31, 61-103 (1991)
3. 3. Boyer, C.P., Plebański, J.F.: Heavens and their integral manifolds. J. Math. Phys. 18, 1022-1031 (1977)
4. 4. Boyer, C.P., Plebański, J.F.: An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces. J. Math. Phys. 26, 229-234 (1985)
5. 5. Boyer, C., Winternitz, P.: Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups. J. Math. Phys. 30, 1081-1094 (1989)
6. 6. Dunajski, M.: The Nonlinear Graviton Construction as an Integrable System. DPhil thesis, Oxford University, 1998
7. 7. Dunajski, M.: The Twisted Photon Associated to Hyper-hermitian Four Manifolds. J. Geom. Phys. 30, 266-281 (1999)
8. 8. Dunajski, M., Mason, L.J.: Heavenly Hierarchies and Curved Twistor Spaces. Twistor Newsletter 41 (1996)
9. A(n). Twistor Newsletter 42 ( 1997)
10. 10. Dunajski, M., Mason, L.J.: A Recursion Operator for ASD Vacuums and Z.R.M Fields on ASD Backgrounds. Twistor Newsletter 43 (1997)
11. 11. Dunajski, M. Mason, L.J., Woodhouse, N.M.J.: From 2D Integrable Systems to Self-Dual Gravity. J. Phys. A: Math. Gen. 31, 6019 (1998)
12. 12. Gindikin, S.: On one construction of hyperKähler metrics. Funct. Anal. Appl. 20, 82-132 (1986)
13. 13. Grant, J.D.E.: On Self-Dual Gravity. Phys. Rev. D48, 2606-2612 (1993)
14. 14. Ko, B., Ludvigsen, M., Newman, E.T., Tod, K.P.: The theory of H space. Phys. Rep. 71 51-139 (1981)
15. 15. Kodaira, K.: On stability of compact submanifolds of complex manifolds. Am. J. Math. 85, 79-94 (1963)
16. 16. Magri, F.: A simple model of the integrable Hamiltonian equation. J. Math. Phys. 19, 1156-1162 (1978)
17. 17. Mason, L.J.: H-space, a universal integrable system? Twistor Newsletter 30 (1990)
18. 18. Mason, L.J., Newman, E.T.: A connection between the Einstein and Yang-Mills equations. Commun. Math. Phys. 121, 659-668 (1989)
19. 19. Mason, L.J., Sparling, G.A.J.: Twistor correspondences for the soliton hierarchies. J. Geom. Phys. 8, 243-271 (1992)
20. 20. Mason, L.J., Woodhouse, N.M.J.: lntegrability, Self-Duality, and Twistor Theory. L.M.S. Monographs New Series, 15. Oxford: OUP, 1996
21. 21. Park, Q.H.: Self-Dual Gravity as a Large-N Limit of the 2D Non-Linear Sigma Model. Phys. Lett. 238A, 287-290 (1990)
22. 22. Penrose, R.: Zero rest-mass fields including gravitation: Asymptotic behaviour. Proc. Roy. Soc. London A284, 159-203 (1965)
23. 23. Penrose, R.: Nonlinear gravitons and curved twistor theory. Gen. Rel. Grav. 7, 31-52 (1976)
24. 24. Penrose, R., Rindler, W.: Spinors and Space-Time, Vol 1, 2. Cambridge: CUP, 1986
25. 25. Plebanski, J.F.: Some solutions of complex Einstein Equations. J. Math. Phys. 16, 2395-2402 (1975)
26. 26. Strachan, I.A.B.: The Symmetry Structure of the Anti-Self-Dual Einstein Hierarchy. J. Math. Phys. 36, 3566-3573 (1995)
27. 27. Sparling, G. A., Tod, K.P.: An example of an H-space. J. Math. Phys. 22, 331-332 (1981)
28. 28. Takasaki, K.: An infinite number of hidden variables in hyper-Kähler metrics. J. Math. Phys. 30, 1515-1521 (1989)
29. 29. Takasaki, K.: Symmetries of hyper-Kähler (or Poisson gauge field ) hierarchy. J. Math. Phys. 31, 1877-1888 (1990)
30. 30. Tod, K.P., Ward, R.S.: Self-dual metrics with self-dual Killing vectors. Proc. R. Soc. A 368, 411-427 (1979)
31. 31. Ward, R.S.: On self-dual gauge fields. Phys. Lett. A 61, 81-82 (1977)
32. 32. Ward, R.S.: Integrable and solvable systems and relations among them. Phil. Trans. R. Soc. A 315, 451-457 (1985)