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Invariant Sp(1)-instantons on S 2 × S 2


In this paper all (anti)self-dual invariant connections on homogeneous quaternionic line bundles over S 2 × S 2 are calculated and described in terms of the isotropy homomorphism of the bundle using Wang's theorem. These are the canonical connections on bundles with an ‘(anti)symmetric twist’ and an S 1-parametrized family of flat structures on bundles with a ‘simple twist’.

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  1. Atiah, M. F., Hitchin, N. J. and Singer, I. M., ‘Self-duality in Four-Dimensional Riemannian Geometry’, Proc. Roy. Soc. London Ser.A, 362 (1978), 425–461.

    Google Scholar 

  2. Itoh, M., ‘On the Moduli Space of Antiself-dual Connections on Kähler Surfaces’, Publ. Res. Inst. Math. Sci., Kyoto University 19 (1983), 15–32.

    Google Scholar 

  3. Itoh, M., ‘Invariant Connections and Yang-Mills Solutions’, Trans. Amer. Math. Soc. 267, No. 1 (1981).

    Google Scholar 

  4. Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, vol. 1, Interscience, New York, 1963.

    Google Scholar 

  5. Freed, D. S., and Uhlenbeck, K. K., Instantons and Four-Manifolds, Springer, Berlin, Heidelberg, New York, 1984.

    Google Scholar 

  6. Atiah, M. F., Geometry of Yang-Mills Fields, Scuola Normale Superiore Pisa, 1979.

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Unger, F.R. Invariant Sp(1)-instantons on S 2 × S 2 . Geom Dedicata 23, 365–368 (1987).

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  • Line Bundle
  • Canonical Connection
  • Flat Structure
  • Invariant Connection
  • Quaternionic Line