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On the geometry of the space of Sp(1)-instantons with Pontrjagin index 1 in the 4-sphere

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Abstract

The geometry of the space ofSp(1)-instantons with index 1 on the 4-sphere is considered. The Riemannian metric of this space is described and conclusions concerning the conformal structure are deduced.

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References

  1. Atiyah, M. F.: Geometry of Yang-Mills Fields. Pisa, Accademia Nazionale dei Lincei, Scuola Normale Superiore, 1979.

    Google Scholar 

  2. Atiyah, M. F.; Hitchin, N. J.; Singer, I. M.: Self-duality in four-dimensional Riemannian Geometry. Proc. Roy. Soc. London, Ser. A 362 (1978), 425–461.

    Google Scholar 

  3. Babelon, O.; Viallet, C. M.: The Riemannian geometry of the configuration space of gauge theories. Commun. Math. Phys. 81 (1981), 515–525.

    Google Scholar 

  4. Bérard-Bergery, L.: Sur le nouvelles variétés riemannienes d'Einstein. Publications de l'Institut Elie Cartan, Nancy 4 (1982), 1–60.

    Google Scholar 

  5. Bourguignon, J. P.; Lawson, H. B. Jr: Stability and isolation phenomena for Yang-Mills fields. Commun. Math. Phys. 79 (1981), 189–230.

    Google Scholar 

  6. Dieudonné, J.: Grundzüge der modernen Analysis 5/6. Braunschweig-Wiesbaden: Friedr. Vieweg & Sohn/Berlin: VEB Deutscher Verlag der Wissenschaften, 1979.

    Google Scholar 

  7. Eisenhart, L. P.: Riemannian Geometry. Princeton: Princeton Univ. Press, 1949.

    Google Scholar 

  8. Friedrich, TH.: Self-duality of Riemannian manifolds and connections. In: Self-dual Riemannian Geometry and Instantons. Leipzig: BSB B. G. Teubner Verlagsgesellschaft, 1981.

    Google Scholar 

  9. Gromoll, D.; Klingenberg, W.; Meyer, W.: Riemannsche Geometry im Groβen. Berlin: Springer-Verlag, 1968 (Lect. Notes Math., 55).

    Google Scholar 

  10. Kobayashi, S.; Nomizu, K.: Foundations of Differential Geometry, Vol. I. New York, London: Interscience Publishers, 1963.

    Google Scholar 

  11. Kondracki, W.; Rogulski, J.: On the Stratification of the Orbit Space for the Action of Automorphisms on Connections. Warszawa, 1983 (Preprint PAN 281).

  12. O'Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13 (1966), 459–469.

    Google Scholar 

  13. Salamon, S. M.: Topics in Four-Dimensional Riemannian Geometry. Pisa, 1982 (Preprint Scuola normale Superiore).

  14. Wallach, N. R.: Harmonic Analysis on Homogeneous Spaces. New York: M. Dekker, Inc., 1973.

    Google Scholar 

  15. Zelobenko, D. P.: Kompaktnye gruppy Li i ich predstavlenija. Moskva: Nauka, 1970.

    Google Scholar 

  16. Zelobenko, D. P.: Stern, A. I.: Predstavlenija grupp Li. Moskva: Nauka, 1983.

    Google Scholar 

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  1. Sektion Mathematik, Bereich Geometrie, Humboldt-Universität zu Berlin, DDR-1086, PF 1297, Berlin

    Lutz Habermann

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  1. Lutz Habermann
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Habermann, L. On the geometry of the space of Sp(1)-instantons with Pontrjagin index 1 in the 4-sphere. Ann Glob Anal Geom 6, 3–29 (1988). https://doi.org/10.1007/BF00054606

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  • DOI: https://doi.org/10.1007/BF00054606

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