Twistor theory of hyper-Kähler metrics with hidden symmetries

Journal of Mathematical Physics

Volumn 44, Issue 8, 2003, Pages 3430-3454

  Dunajski, Maciej ^a   Mason, Lionel J ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041728678     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1588466     Document Type: Review

References (32)

1. Akivis, M., "Nets and almost Grassmanian structures," Proc Natl. Acad. USSR 252, 2, 267-270 (1980).
2. Bailey, T. N., and Eastwood, M. G., "Complex Paraconformal manifolds, their differential geometry and twistor theory," Forum Math. 3, 61-103 (1991).
3. Bielawski, R., Twistor Quotients of Hyper-Kähler Manifolds (World Scientific, River Edge, NJ, 2001).
4. Bielawski, R., and Calderbank, D., "Hypercomplex manifolds with symmetry," preprint.
5. Boyer, C. P., and 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).
6. Brieskorn, E., "Singular elements of semisimple algebraic groups," Actes Congres Intern. Math. 2, 279-284 (1970).
7. Dunajski, M., "Anti-self-dual 4-manifolds with a parallel real spinor," Proc. R. Soc. London, Ser. A 458 (2021), 1205-1222 (2002).
8. Dunajski, M., and Mason, L. J., "Hyper-Kähler Hierarchies and their twistor theory," Commun. Math. Phys. 213, 641-672 (2000).
9. Dunajski, M., and Tod, K. P., "Einstein-Weyl Structures from Hyper-Kähler Metrics with conformal Killing Vectors," Diff. Geom. Applic. 14, 39-55 (2001).
10. Dunajski, M., Mason, L. J., and Tod, K. P., "Einstein-Weyl geometry, the dKP equation and twistor theory," J. Geom. Phys. 37, 63-92 (2001).
11. Finley, J. D., and Plebański, J. F., "The classification of all ℋ spaces admitting a Killing vector," J. Math. Phys, 20, 1938 (1979).
12. Gibbons, G. W., and Hawking, S. W., "Gravitational multi-instantons," Phys. Lett. B 78B, 430-432 (1978).
13. Gindikin, S., "Bundles of differential forms and the Einstein equation," Sov. J. Nucl. Phys. 36 (2), 313-319 (1982).
14. Gindikin, S., "Generalized conformal structures," in Twisters in Mathematics and Physics, edited by T. N. Bailey and R. J. Baston, LMS Lecture Notes Series Vol. 156 (Cambridge University Press, Cambridge, 1990).
15. Hitchin, N., "Polygons and gravitons," Math. Proc. Cambridge Philos. Soc. 85, 456-476 (1979).
16. Hitchin, N. J., Karlhede, A., Lindstrom, U., and Rocek, M., "Hyper-Kähler metrics and supersymmetry," Commun. Math. Phys. 108, 535-589 (1987).
17. Ivanov, I. T., and Rocek, M., "Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric," Commun. Math. Phys. 182, 291-302 (1996).
18. Kronheimer, P., "The Construction of ALE Spaces as Hyper-Kähler Quotient," J. Diff. Geom. 29, 665 (1989).
19. Kronheimer, P., "A Torelli Type Theorem For Gravitational Instantons," J. Diff. Geom. 29, 685 (1989).
20. Lindstrom, U., and Rocek, M., "New hyper-Kähler metrics and new supermultiplets," Commun. Math. Phys. 115, 21-29 (1988).
21. Mason, L. J., and Woodhouse, N. M. J., Integrability, Self-duality and Twistor Theory, LMS Monograph (Cambridge University Press, Cambridge, 1996).
22. Merkulov, S., "Existence and geometry of Legendre Moduli spaces," Math. Z. 226, 211-265 (1997).
23. Merkulov, S., "Affine connections on involutive G-structures," in Geometry and Physics (Aarhus, 1995), Lecture Notes in Pure and Appl. Math. Vol. 184 (Dekker, New York, 1997), pp. 261-274.
24. Novikov, S. P., "The periodic problem for the Korteweg-de Vries equation," Funct. Anal. Appl. 8, 236-246 (1974).
25. Penrose, R., "Nonlinear gravitons and curved twistor theory," Gen. Relativ. Gravit. 7, 31-52 (1976).
26. Penrose, R., and Rindler, W., Spinors and Space-Time, Vols. 1 and 2 (Cambridge University Press, Cambridge, 1986).
27. Plebanski, J. F., "Some solutions of complex Einstein equations," J. Math. Phys. 16, 2395-2402 (1975).
28. Salamon, S. M., "Quaternionic Kähler manifolds," Invent. Math. 67, 143-171 (1982).
29. Strachan, I. A. B., "The symmetry structure of the anti-self-dual Einstein hierarchy," J. Math. Phys. 36, 3566-3573 (1995).
30. Takasaki, K., "An infinite number of hidden variables in hyper-Kähler metrics," J. Math. Phys. 30, 1515-1521 (1989).
31. Tod, K. P., and Ward, R. S., "Self-dual metrics with self-dual Killing vectors," Proc. R. Soc. London, Ser. A 368, 411-427 (1979).
32. Ward, R. S., "A class of self-dual solutions of Einstein's equations," Proc. R. Soc. London, Ser. A 363, 289-295 (1978).