Curvature of hyperkähler quotients

Roger Bielawski

Open Mathematics (2008)

  • Volume: 6, Issue: 2, page 191-203
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Roger Bielawski. "Curvature of hyperkähler quotients." Open Mathematics 6.2 (2008): 191-203. <http://eudml.org/doc/269557>.

@article{RogerBielawski2008,
abstract = {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.},
author = {Roger Bielawski},
journal = {Open Mathematics},
keywords = {hyperkaehler manifolds; monopoles; Hitchin’s equations; infinite-dimensional manifolds; Nahm's equations},
language = {eng},
number = {2},
pages = {191-203},
title = {Curvature of hyperkähler quotients},
url = {http://eudml.org/doc/269557},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Roger Bielawski
TI - Curvature of hyperkähler quotients
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 191
EP - 203
AB - 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.
LA - eng
KW - hyperkaehler manifolds; monopoles; Hitchin’s equations; infinite-dimensional manifolds; Nahm's equations
UR - http://eudml.org/doc/269557
ER -

References

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  2. [2] Besse A.L., Einstein manifolds, Springer Verlag, Berlin, 1987 Zbl0613.53001
  3. [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 Zbl0603.58042
  4. [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. [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 Zbl0634.53045
  6. [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 Zbl0824.58015
  7. [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 Zbl0772.53011
  8. [8] Lang S., Fundamentals of differential geometry, Springer Verlag, New York, 1999 Zbl0932.53001
  9. [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. [10] Swartz C., Continuity and hypocontinuity for bilinear maps, Math. Z., 1984, 186, 321–329 http://dx.doi.org/10.1007/BF01174886 Zbl0545.46004

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