Communications in Mathematical Physics

, Volume 83, Issue 4, pp 579–602 | Cite as

Monopoles and geodesics

  • N. J. Hitchin


Using the holomorphic geometry of the space of straight lines in Euclidean 3-space, it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve by means of the Atiyah-Ward Ansatz\(A_k \).


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Proc. R. Soc. Lond. A362, 425–461 (1978)Google Scholar
  2. 2.
    Atiyah, M.F., Hitchin, N.J., Drinfeld, V.G., Manin, Yu.I.: Phys. Lett.65A, 185 (1978)Google Scholar
  3. 3.
    Atiyah, M.F., Ward, R.S.: Commun. Math. Phys.55, 117 (1977)Google Scholar
  4. 4.
    Bogomolny, E.B.: Sov. J. Nucl. Phys.24, 449 (1976)Google Scholar
  5. 5.
    Coddington, E.A., Levinson, N.: Theory of ordinary differential equations. New York: McGraw-Hill 1955Google Scholar
  6. 6.
    Coppel, W.A.: Stability and asymptotic behaviour of differential equations. Boston: D.C. Heath & Co. 1965Google Scholar
  7. 7.
    Corrigan, E., Goddard, P.: Commun. Math. Phys.80, 575–587 (1981)Google Scholar
  8. 8.
    Eisenhart, L.P.: A treatise on the differential geometry of curves and surfaces. Boston: Ginn & Co. 1909Google Scholar
  9. 9.
    Forgacs, P., Horvath, Z., Palla, L.: Phys. Lett.102B, 131 (1981)Google Scholar
  10. 10.
    Hitchin, N.J.: Proceedings of conference on gauge theories. Primorsko, Bulgaria 1980 (to appear)Google Scholar
  11. 11.
    Nahm, W.: Phys. Lett.90B, 413–414 (1980)Google Scholar
  12. 12.
    Prasad, M.K., Rossi, P.: MIT preprint CTP 903, 1980Google Scholar
  13. 13.
    Prasad, M.K., Sommerfield, C.M.: Phys. Rev. Lett.35, 760 (1975)Google Scholar
  14. 14.
    Ward, R.S.: Phys. Lett.61A, 81 (1977)Google Scholar
  15. 15.
    Ward, R.S.: Commun. Math. Phys.79, 317–325 (1981)Google Scholar
  16. 16.
    Ward, R.S.: Phys. Lett. B (to appear)Google Scholar
  17. 17.
    Weierstrass, K.: Monatsberichte der Berliner Akademie 612–625 (1866)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • N. J. Hitchin
    • 1
  1. 1.St. Catherine's CollegeOxfordEngland

Personalised recommendations