Hyper-Hamiltonian dynamics

Journal of Physics A: Mathematical and General

Volumn 35, Issue 17, 2002, Pages 3925-3943

  Gaeta, Giuseppe ^a,b   Morando, Paola ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

^c POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037013170     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/35/17/308     Document Type: Article

References (47)

1. Abraham R and Marsden J E 1967, 1978 Foundations of Mechanics (New York: Benjamin)
2. Alekseevsky D V and Marchiafava S 1996 Quaternionic structures on a manifold and subordinated structures Ann. Mat. Pura Appl. 171 205-73
3. Arnold V I 1978, 1989 Mathematical Methods of Classical Mechanics (Berlin: Springer)
4. Arnold V I 1983, 1989 Geometrical Methods in the Theory of Ordinary Differential Equations (Berlin: Springer)
5. Arnold V I and Givental A B 1990 Symplectic geometry Dynamical Systems vol 4, EMS 4, ed V I Arnol'd and S P Novikov (Berlin: Springer)
6. Arnold V I, Kozlov V V and Neishtadt A I 1993, 1997 Mathematical aspects of classical and celestial mechanics Dynamical Systems vol 3, EMS 3, ed V I Arnol'd (Berlin: Springer)
7. Atiyah M F 1979 Geometry of Yang-Mills Fields (Lezioni Fermiane) (Pisa: Scuola Normale Superiore)
8. Atiyah M F 1990 Hyper-Kahler manifolds Complex Geometry and Analysis (Lecture Notes in Mathematics 1422) ed V Villani (Berlin: Springer)
9. Atiyah M F and Hitchin N J 1988 The Geometry and Dynamics of Magnetic Monopoles (Princeton, NJ: Princeton University Press)
10. Bielawski R 1997 HyperKahler structures and group actions J. Lond. Math. Soc. 55 400-14
11. Bredon G E 1993 Topology and Geometry (New York: Springer)
12. Calabi E 1979 Métriques Kahlériennes et fibrés holomorphes Ann. Sci. Ecole Norm. Sup. Paris IV 12 269-94
13. Calabi E 1980 Isometric families of Kahler structures Chern Symp. (1979) ed W-Y Hsiang et al (New York: Springer)
14. Cannas da Silva A 2001 Lectures on Symplectic Geometry (Lecture Notes in Mathematics 1764) (Berlin: Springer)
15. Cartan E 1945, 1971 Les Systémes Différentielles Extérieurs et leurs Applications Géométriques (Paris: Hermann)
16. Cecotti S, Ferrara S and Girardello L 1989 Geometry of type II superstrings and the moduli space of superconformal theories Int. J. Mod. Phys. A 4 2475-529 Anselmi D and Fré P 1994 Topological sigma-models in four dimensions and triholomorphic maps Nucl. Phys. B 416 255-300 Ivanov I T and Rocek M 1996 Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric Commun. Math. Phys. 182 291-302 Antoniadis I and Pioline B 1997 Higgs branch, hyperKahler quotients and duality in SUSY N = 2 Yang-Mills theories Int. J. Mod. Phys. A 12 4907-32 Hitchin N J 1999 The moduli space of complex Lagrangian submanifolds Asian J. Math. 3 77-91 Alexseevsky D V, Cortés V, Devchand C and van Proeyen A 2001 Flows on quaternionic-Kahler and very special real manifolds Preprint arXiv hep-th/0109094
17. Cecotti S, Ferrara S and Girardello L 1989 Geometry of type II superstrings and the moduli space of superconformal theories Int. J. Mod. Phys. A 4 2475-529 Anselmi D and Fré P 1994 Topological sigma-models in four dimensions and triholomorphic maps Nucl. Phys. B 416 255-300 Ivanov I T and Rocek M 1996 Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric Commun. Math. Phys. 182 291-302 Antoniadis I and Pioline B 1997 Higgs branch, hyperKahler quotients and duality in SUSY N = 2 Yang-Mills theories Int. J. Mod. Phys. A 12 4907-32 Hitchin N J 1999 The moduli space of complex Lagrangian submanifolds Asian J. Math. 3 77-91 Alexseevsky D V, Cortés V, Devchand C and van Proeyen A 2001 Flows on quaternionic-Kahler and very special real manifolds Preprint arXiv hep-th/0109094
18. Cecotti S, Ferrara S and Girardello L 1989 Geometry of type II superstrings and the moduli space of superconformal theories Int. J. Mod. Phys. A 4 2475-529 Anselmi D and Fré P 1994 Topological sigma-models in four dimensions and triholomorphic maps Nucl. Phys. B 416 255-300 Ivanov I T and Rocek M 1996 Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric Commun. Math. Phys. 182 291-302 Antoniadis I and Pioline B 1997 Higgs branch, hyperKahler quotients and duality in SUSY N = 2 Yang-Mills theories Int. J. Mod. Phys. A 12 4907-32 Hitchin N J 1999 The moduli space of complex Lagrangian submanifolds Asian J. Math. 3 77-91 Alexseevsky D V, Cortés V, Devchand C and van Proeyen A 2001 Flows on quaternionic-Kahler and very special real manifolds Preprint arXiv hep-th/0109094
19. Cecotti S, Ferrara S and Girardello L 1989 Geometry of type II superstrings and the moduli space of superconformal theories Int. J. Mod. Phys. A 4 2475-529 Anselmi D and Fré P 1994 Topological sigma-models in four dimensions and triholomorphic maps Nucl. Phys. B 416 255-300 Ivanov I T and Rocek M 1996 Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric Commun. Math. Phys. 182 291-302 Antoniadis I and Pioline B 1997 Higgs branch, hyperKahler quotients and duality in SUSY N = 2 Yang-Mills theories Int. J. Mod. Phys. A 12 4907-32 Hitchin N J 1999 The moduli space of complex Lagrangian submanifolds Asian J. Math. 3 77-91 Alexseevsky D V, Cortés V, Devchand C and van Proeyen A 2001 Flows on quaternionic-Kahler and very special real manifolds Preprint arXiv hep-th/0109094
20. Cecotti S, Ferrara S and Girardello L 1989 Geometry of type II superstrings and the moduli space of superconformal theories Int. J. Mod. Phys. A 4 2475-529 Anselmi D and Fré P 1994 Topological sigma-models in four dimensions and triholomorphic maps Nucl. Phys. B 416 255-300 Ivanov I T and Rocek M 1996 Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric Commun. Math. Phys. 182 291-302 Antoniadis I and Pioline B 1997 Higgs branch, hyperKahler quotients and duality in SUSY N = 2 Yang-Mills theories Int. J. Mod. Phys. A 12 4907-32 Hitchin N J 1999 The moduli space of complex Lagrangian submanifolds Asian J. Math. 3 77-91 Alexseevsky D V, Cortés V, Devchand C and van Proeyen A 2001 Flows on quaternionic-Kahler and very special real manifolds Preprint arXiv hep-th/0109094
21. Cecotti S, Ferrara S and Girardello L 1989 Geometry of type II superstrings and the moduli space of superconformal theories Int. J. Mod. Phys. A 4 2475-529 Anselmi D and Fré P 1994 Topological sigma-models in four dimensions and triholomorphic maps Nucl. Phys. B 416 255-300 Ivanov I T and Rocek M 1996 Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric Commun. Math. Phys. 182 291-302 Antoniadis I and Pioline B 1997 Higgs branch, hyperKahler quotients and duality in SUSY N = 2 Yang-Mills theories Int. J. Mod. Phys. A 12 4907-32 Hitchin N J 1999 The moduli space of complex Lagrangian submanifolds Asian J. Math. 3 77-91 Alexseevsky D V, Cortés V, Devchand C and van Proeyen A 2001 Flows on quaternionic-Kahler and very special real manifolds Preprint arXiv hep-th/0109094
22. Dancer A S 1993 Nahm's equations and hyperKahler geometry Commun. Math. Phys. 158 545-68
23. Fomenko A T 1988, 1995 Symplectic Geometry (New York: Gordon and Breach)
24. Freed D S 1999 Special Kahler manifolds Commun. Math. Phys. 203 31-52
25. Gentili G, Marchiafava S and Pontecorvo M (ed) 1994 Proc. Meeting on Quaternionic Structures in Mathematics and Physics (Trieste, 1994) (EMS Electronic Library) Marchiafava S, Piccinni P and Pontecorvo M 1999 Proc. 2nd Meeting on Quaternionic Structures in Mathematics and Physics (Roma, 1999) (EMS Electronic Library) Marchiafava S, Piccinni P and Pontecorvo M (ed) 2001 Quaternionic Structures in Mathematics and Physics (Singapore: World Scientific)
26. Gentili G, Marchiafava S and Pontecorvo M (ed) 1994 Proc. Meeting on Quaternionic Structures in Mathematics and Physics (Trieste, 1994) (EMS Electronic Library) Marchiafava S, Piccinni P and Pontecorvo M 1999 Proc. 2nd Meeting on Quaternionic Structures in Mathematics and Physics (Roma, 1999) (EMS Electronic Library) Marchiafava S, Piccinni P and Pontecorvo M (ed) 2001 Quaternionic Structures in Mathematics and Physics (Singapore: World Scientific)
27. Gentili G, Marchiafava S and Pontecorvo M (ed) 1994 Proc. Meeting on Quaternionic Structures in Mathematics and Physics (Trieste, 1994) (EMS Electronic Library) Marchiafava S, Piccinni P and Pontecorvo M 1999 Proc. 2nd Meeting on Quaternionic Structures in Mathematics and Physics (Roma, 1999) (EMS Electronic Library) Marchiafava S, Piccinni P and Pontecorvo M (ed) 2001 Quaternionic Structures in Mathematics and Physics (Singapore: World Scientific)
28. Giordano M, Marmo G and Rubano C 1993 The inverse problem in the Hamiltonian formalism: integrability of linear Hamiltonian fields Inverse Problems 9 443-67
29. Godbillon C 1969 Géometrie Différentielle et Mécanique Analitique (Paris: Hermann)
30. Gotay M J, Isenberg J and Marsden J E 1998 Momentum maps and classical relativistic fields. I: covenant field theory Preprint arXiv physics/9801019
31. Guillemin V and Sternberg S 1984 Symplectic Techniques in Physics (Cambridge: Cambridge University Press)
32. Hermann R 1968 Differential Geometry and the Calculus of Variations (New York: Academic) (1977 Brookline: Math Sci Press)
33. Hitchin N J 1987 The self-duality equation on a Riemann surface Proc. Lond. Math. Soc. 55 59-126
34. Hitchin N J, Karlhede A, Linstrom U and Rocek M 1987 Hyper Kahler metrics and supersymmetry Commun. Math. Phys. 108 535-89
35. Linstrom U, Rocek M and von Unge R 2000 HyperKahler quotients and algebraic curves J. High Energy Phys. JHEP01(2000)022
36. Morando P and Tarallo M 2002 Quaternionic Hamilton equations Preprint arXiv math-ph/0204021
37. Penrose R 1967 Twistor algebra J. Math. Phys. 8 345-66 Penrose R and MacCallum M A H 1973 Twistor theory: an approach to the quantisation of fields and space-time Phys. Rep. 6 241-316 Penrose R and Rindler W 1984 Spinors and Space-Time vol 2 (Cambridge: Cambridge University Press)
38. Penrose R 1967 Twistor algebra J. Math. Phys. 8 345-66 Penrose R and MacCallum M A H 1973 Twistor theory: an approach to the quantisation of fields and space-time Phys. Rep. 6 241-316 Penrose R and Rindler W 1984 Spinors and Space-Time vol 2 (Cambridge: Cambridge University Press)
39. Penrose R 1967 Twistor algebra J. Math. Phys. 8 345-66 Penrose R and MacCallum M A H 1973 Twistor theory: an approach to the quantisation of fields and space-time Phys. Rep. 6 241-316 Penrose R and Rindler W 1984 Spinors and Space-Time vol 2 (Cambridge: Cambridge University Press)
40. Salamon S M 1982 Quaternionic Kahler manifolds Invent. Math. 67 143-71 Salamon S M 1986 Differential geometry of quaternionic manifolds Ann. Sci. Ecole Norm. Sup. IV 19 31-55
41. Salamon S M 1982 Quaternionic Kahler manifolds Invent. Math. 67 143-71 Salamon S M 1986 Differential geometry of quaternionic manifolds Ann. Sci. Ecole Norm. Sup. IV 19 31-55
42. Saunders D J 1989 The Geometry of Jet Bundles (Cambridge: Cambridge University Press)
43. Swann A 1991 HyperKahler and quaternionic Kahler geometry Math. Ann. 289 421-50 Swann A 1989 Aspects symplectiques de la géométrie quaternionique C. R. Acad. Sci., Paris 308 225-8
44. Swann A 1991 HyperKahler and quaternionic Kahler geometry Math. Ann. 289 421-50 Swann A 1989 Aspects symplectiques de la géométrie quaternionique C. R. Acad. Sci., Paris 308 225-8
45. Verbitsky M and Kaledin D 1999 HyperKahler Manifolds (Somerville: International)
46. Ward R S and Wells R O 1990 Twistor Geometry and Field Theory (Cambridge: Cambridge University Press)
47. Xu P 1997 Hyper-Lie Poisson structures Ann. Sci. Ecole Norm. Sup. 30 279-302