Curvature of hyperkähler quotients

• Autorzy: Roger Bielawski
• Języki publikacji: EN

Abstrakty

EN

We prove estimates for the sectional curvature of hyperkähler quotients and give applications to moduli spaces of solutions to Nahm’s equations and Hitchin’s equations.

Słowa kluczowe

EN

hyperkaehler manifolds; monopoles; Hitchin’s equations; infinite-dimensional manifolds

Kategorie tematyczne

• 81T13: Yang-Mills and other gauge theories
• 53C26: Hyper-K\"ahler and quaternionic K\"ahler geometry, ``special'' geometry

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 191-203

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Roger Bielawski

Bibliografia

• [1] Aubin T., Nonlinear analysis on manifolds. Monge-Ampère equations, Springer Verlag, New York, 1982
• [2] Besse A.L., Einstein manifolds, Springer Verlag, Berlin, 1987
• [3] Donaldson S.K., Nahm’s equations and the classification of monopoles, Comm. Math. Phys., 1984, 96, 387–407 http://dx.doi.org/10.1007/BF01214583
• [4] Donaldson S.K., Boundary value problems for Yang-Mills fields, J. Geom. Phys., 1992, 8, 89–122 http://dx.doi.org/10.1016/0393-0440(92)90044-2
• [5] Hitchin N.J., The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 1987, 55, 59–126 http://dx.doi.org/10.1112/plms/s3-55.1.59
• [6] Hurtubise J.C., The classification of monopoles for the classical groups, Comm. Math. Phys., 1989, 120, 613–641 http://dx.doi.org/10.1007/BF01260389
• [7] Jost J., Peng X.-W., Group actions gauge transformations and the calculus of variations, Math. Ann., 1992, 293, 595–621 http://dx.doi.org/10.1007/BF01444737
• [8] Lang S., Fundamentals of differential geometry, Springer Verlag, New York, 1999
• [9] Nahm W., The construction of all self-dual multimonopoles by the ADHM method, in: Monopoles in quantum field theory, World Sci. Publishing, Singapore, 1982, 87–94
• [10] Swartz C., Continuity and hypocontinuity for bilinear maps, Math. Z., 1984, 186, 321–329 http://dx.doi.org/10.1007/BF01174886

Identyfikatory

DOI

10.2478/s11533-008-0026-8