Hyperkähler manifolds

Nigel Hitchin

Séminaire Bourbaki (1991-1992)

  • Volume: 34, page 137-166
  • ISSN: 0303-1179

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Hitchin, Nigel. "Hyperkähler manifolds." Séminaire Bourbaki 34 (1991-1992): 137-166. <http://eudml.org/doc/110151>.

@article{Hitchin1991-1992,
author = {Hitchin, Nigel},
journal = {Séminaire Bourbaki},
keywords = {twistor construction; hyper-Kähler quotient; hyper-Kähler manifold; resolution of singularities; coadjoint orbits; complex Lie groups; moduli spaces of connections},
language = {eng},
pages = {137-166},
publisher = {Société Mathématique de France},
title = {Hyperkähler manifolds},
url = {http://eudml.org/doc/110151},
volume = {34},
year = {1991-1992},
}

TY - JOUR
AU - Hitchin, Nigel
TI - Hyperkähler manifolds
JO - Séminaire Bourbaki
PY - 1991-1992
PB - Société Mathématique de France
VL - 34
SP - 137
EP - 166
LA - eng
KW - twistor construction; hyper-Kähler quotient; hyper-Kähler manifold; resolution of singularities; coadjoint orbits; complex Lie groups; moduli spaces of connections
UR - http://eudml.org/doc/110151
ER -

References

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  1. [AHS] M.F. Atiyah, N.J. Hitchin and I.M. Singer - Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. Lond. A362 (1978), 425-461. Zbl0389.53011MR506229
  2. [AB] M.F. Atiyah and R. Bott - The Yang-Mills equations over Riemann surfaces, Phil. Trans. Roy. Soc. Lond. A308 (1982), 523-615. Zbl0509.14014MR702806
  3. [AH] M.F. Atiyah and N.J. Hitchin - "The geometry and dynamics of magnetic monopoles ", Princeton University Press, Princeton (1988). Zbl0671.53001MR934202
  4. [Bea] A. Beauville - Variétés Kählériennes dont la 1ère classe de Chern est nulle, J. Diff. Geometry18 (1983), 755-782. Zbl0537.53056MR730926
  5. [Be] A. Besse - "Einstein manifolds", Springer Verlag, Berlin (1987). Zbl0613.53001MR867684
  6. [Bo] S. Bochner - Curvature in Hermitian metric, Bull. Amer. Math. Soc.53 (1947) 179-195. Zbl0035.10403MR19983
  7. [Bu] D. Burns - Some examples of the twistor construction, in "Contributions to several complex variables: in honor of Wilhelm Stoll" (eds. A. Howard and P. -M. Wong), Vieweg, Braunschweig (1986). Zbl0596.53057MR859192
  8. [BvB] P.J. Braam and P. van Baal - Nahm's transformation for instantons, Commun. Math. Phys.122 (1989), 267-280. Zbl0672.55009MR994505
  9. [Ca] E. Calabi - Métriques kählériennes et fibrés holomorphes, Ann. Éc. Norm. Sup.12 (1979) 269-294. Zbl0431.53056MR543218
  10. [Co] K. Corlette - Flat G-bundles with canonical metrics, J. Diff. Geometry28 (1988) 351-382. Zbl0676.58007MR965220
  11. [D1] S.K. Donaldson - Nahm's equations and the classification of monopoles, Commun. Math. Phys.96 (1984) 387-407. Zbl0603.58042MR769355
  12. [D2] S.K. Donaldson - Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc.55 (1987) 127-131. Zbl0634.53046MR887285
  13. [D3] S.K. Donaldson - Boundary value problems for Yang-Mills fields, preprint (Oxford) (1991). MR1165874
  14. [EH] T. Eguchi and A.J. Hanson - Asymptotically flat self-dual solutions to Euclidean gravity, Phys. Lett.74B (1978) 249-251. MR540896
  15. [ES] J. Eells and J.H. Sampson - Harmonic mappings of Riemannian manifolds, Amer. J. Math.86 (1964) 109-160. Zbl0122.40102MR164306
  16. [GL] K. Galicki and H.B. Lawson - Quaternionic reduction and quaternionic orbifolds, Math. Ann.282 (1988) 1-21. Zbl0628.53060MR960830
  17. [G] W.M. Goldman - The symplectic nature of fundamental groups of surfaces, Adv. in Math.54 (1984) 200-225. Zbl0574.32032MR762512
  18. [Gr] A. Gray - A note on manifolds whose holonomy group is a subgroup of Sp(n).Sp(1), Michigan Math. J.16 (1969) 125-128. Zbl0177.50001MR244913
  19. [Ha] R.S. Hamilton - "Harmonic maps of manifolds with boundary", Lecture Notes in Mathematics471, Springer Verlag, Berlin (1975). Zbl0308.35003MR482822
  20. [H] W.R. Hamilton - letter to P. G. Tait, October 15th, 1858. 
  21. [H1] N.J. Hitchin - Polygons and gravitons, Math. Proc. Camb. Phil. Soc.85 (1979) 465-476. Zbl0405.53016MR520463
  22. [H2] N.J. Hitchin - Linear field equations on self-dual spaces, Proc. Roy. Soc. Lond. A370 (1980) 173-191. Zbl0436.53058MR563832
  23. [H3] N.J. Hitchin - On the construction of monopoles, Commun. Math. Phys.89 (1983) 145-190. Zbl0517.58014MR709461
  24. [H4] N.J. Hitchin - Twistor construction of Einstein metrics, in "Global Riemannian geometry" (eds. T. J. Willmore and N. J. Hitchin), Ellis Horwood, Chichester (1984) Zbl0615.53057MR757213
  25. [H5] N.J. Hitchin - The self-duality equations on a Riemann surface, Proc. London Math. Soc.55 (1987) 59-126. Zbl0634.53045MR887284
  26. [HKLR] N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček - Hyperkähler metrics and supersymmetry, Commun. Math. Phys.108 (1987) 535-59. Zbl0612.53043MR877637
  27. [J] D. Joyce - The hypercomplex quotient and the quaternionic quotient, Math. Ann.290 (1991) 323-340. Zbl0723.53043MR1109637
  28. [Ki] F. Kirwan - "Cohomology of quotients in symplectic and algebraic geometry", Princeton University Press, Princeton (1985). Zbl0553.14020MR766741
  29. [K1] P.B. Kronheimer - Instantons gravitationelles et singularités de Klein, C. R. Acad. Sci. Paris Sér. 1 Math.303 (1986) 53-55. Zbl0591.53057MR851268
  30. [K2] P.B. KronheimerThe construction of ALE spaces as hyperkähler quotients, J. Diff. Geometry29 (1989) 665-683. Zbl0671.53045MR992334
  31. [K3] P.B. Kronheimer. - A hyperkählerian structure on coadjoint orbits of a semisimple Lie group, J. London Math. Soc.42 (1990) 193-208. Zbl0721.22006MR1083440
  32. [Ma] A. Maciocia - Metrics on the moduli spaces of instantons over Euclidean 4-space, Commun. Math. Phys.135 (1991) 467-482. Zbl0734.53025MR1091573
  33. [McK] J. McKay - Graphs, singularities and finite groups, Proc. Sympos. Pure Math. Vol. 37, American mathematical Society, Providence (1980) 183-186. Zbl0451.05026MR604577
  34. [N] H. Nakajima - Monopoles and Nahm's equations, preprint (Tokyo) (1991). 
  35. [NS] M.S. Narasimhan and C.S. Seshadri - Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math.82 (1965) 540-567. Zbl0171.04803MR184252
  36. [P] R. Penrose - Nonlinear gravitons and curved twistor theory, Gen. Relativ. Grav.7 (1976) 31-52. Zbl0354.53025MR439004
  37. [PS] A. Pressley and G.B. Segal - "Loop groups", OxfordUniversity Press, Oxford (1986). Zbl0618.22011
  38. [S] S. Salamon - Differential geometry of quaternionic manifolds, Ann. Sci. Éc. Norm. Sup. Paris19 (1986) 31-55. Zbl0616.53023MR860810
  39. [Y] S.T. Yau - On Catabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. USA74 (1977) 1798-1799. Zbl0355.32028MR451180

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