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1997 | 39 | 1 | 143-153
Tytuł artykułu

Singular Moment Maps and Quaternionic Geometry

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
39
Numer
1
Strony
143-153
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
  • School of Mathematical Sciences, University of Bath Claverton Down, Bath BA2 7AY, England
Bibliografia
  • [AH] M. F. Atiyah and N. J. Hitchin, The geometry and dynamics of magnetic monopoles , Princeton University Press, Princeton, 1988.
  • [Ba] F. Battaglia, $S^1$-quotients of quaternion-Kähler manifolds , Proc. Amer. Math. Soc. (to appear).
  • [Bea] A. Beauville, Variétés Kähleriennes dont la 1ère classe de Chern est nulle , J. Differential Geom. 18 (1983), 755-782.
  • [Ber] M. Berger, Sur les groupes d'holonomie des variétés à connexion affines et des variétés riemanniennes , Bull. Soc. Math. France 83 (1955), 279-330.
  • [Ca1] E. Calabi, Métriques Kählériennes et Fibrés Holomorphes , Ann. Scient. École Norm. Sup. (4) 12 (1979), 269-294.
  • [Ca2] E. Calabi, Isometric Families of Kähler Structures , in: The Chern Symposium, 1979, W.-Y. Hsiang et al. (eds.), Springer-Verlag, 1980, 23-39.
  • [Da] A. S. Dancer, Dihedral singularities and gravitational instantons , J. Geom. Phys. 12 (1993) 77-91.
  • [DS1] A. S. Dancer and A. F. Swann, Hyperkähler metrics associated to compact Lie groups , Math. Proc. Cambridge Philos. Soc. (to appear).
  • [DS2] A. S. Dancer and A. F. Swann, The structure of quaternionic Kähler quotients , preprint, 1995.
  • [Ga] K. Galicki, A generalization of the momentum mapping construction for quaternionic Kähler manifolds , Comm. Math. Phys. 108 (1987), 117-138.
  • [GL] K. Galicki and H. B. Lawson, Quaternionic reduction and quaternionic orbifolds , Math. Ann. 282 (1988), 1-21.
  • [GS] V. Guillemin and S. Sternberg, A normal form for the moment map , In: Differential geometric methods in mathematical physics, S. Sternberg (ed.), Reidel Publishing Company, Dordrecht, 1984, 161-175.
  • [H1] N. J. Hitchin, Polygons and Gravitons , Math. Proc. Cambridge Philos. Soc. 85 (1979), 465-476.
  • [H2] N. J. Hitchin, Kählerian twistor spaces , Proc. London Math. Soc. (3) 43 (1981), 133-150.
  • [H3] N. J. Hitchin, The self-duality equations on a Riemann surface , Proc. London Math. Soc. (3) 55 (1987), 59-126.
  • [HKLR] N. J. Hitchin, A. Karlhede, U. Lindström and M. Roček, HyperKähler metrics and supersymmetry , Comm. Math. Phys. 108 (1987), 535-589.
  • [J1] D. D. Joyce, Compact Riemannian 7-manifolds with holonomy $G_2$. I , J. Differential Geom. (to appear).
  • [J2] D. D. Joyce, Compact Riemannian 7-manifolds with holonomy $G_2$. II , J. Differential Geom. (to appear).
  • [J3] D. D. Joyce, Compact Riemannian 8-manifolds with holonomy Spin(7), preprint, 1995.
  • [KS] P. Z. Kobak and A. F. Swann, Classical nilpotent orbits as hyperKähler quotients , Internat. J. Math. 7 (1996), 193-210.
  • [K1] P. B. Kronheimer, A hyperkähler structure on the cotangent bundle of a complex Lie group , MSRI preprint, 1988.
  • [K2] P. B. Kronheimer, The construction of ale spaces as hyperKähler quotients , J. Differential Geom. 29 (1989), 665-683.
  • [K3] P. B. Kronheimer, A Torelli-type theorem for gravitational instantons , J. Differential Geom. 29 (1989), 685-697.
  • [K4] P. B. Kronheimer, Instantons and the geometry of the nilpotent variety , J. Differential Geom. 32 (1990), 473-490.
  • [Le] C. R. LeBrun, On complete quaternionic-Kähler manifolds , Duke Math. J. 63 (1991), 723-743.
  • [LS] C. R. LeBrun and S. M. Salamon, Strong rigidity of positive quaternion-Kähler manifolds , Invent. Math. 118 (1994), 109-132.
  • [Na] H. Nakajima, Instantons on ale spaces, quiver varieties and Kac-Moody algebras , Duke Math. J. 76 (1994), 365-416.
  • [Pa] D. N. Page, A physical picture of the K3 gravitational instanton , Phys. Lett. 80B (1978), 55-57.
  • [PS] Y. S. Poon and S. M. Salamon, Eight-dimensional quaternionic Kähler manifolds with positive scalar curvature , J. Differential Geom. 33 (1991), 363-378.
  • [Sa] S. M. Salamon, Quaternionic Kähler manifolds , Invent. Math. 67 (1982), 143-171.
  • [SL] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction , Ann. of Math. (2) 134 (1991), 375-422.
  • [Sw] A. F. Swann, HyperKähler and quaternionic Kähler geometry , Math. Ann. 289 (1991), 421-450.
  • [Wi] J. A. Wiśniewski, On Fano manifolds of large index , Manuscripta Math. 70 (1991), 145-152.
  • [Wo] J. A. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces , J. Math. Mech. 14 (1965), 1033-1047.
  • [Yau] S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I , Comm. Pure Appl. Math. 31 (1978), 339-411.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv39z1p143bwm
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