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References
Atiyah, M.F., and Bott, R: The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London A, 308 (1982), 523–615.
Atiyah, M.F., Hitchin, N.J., and Singer, I.M.: Self-duality in four dimensional Riemannian geometry, Proc. R. Soc. London A, 362 (1978), 425–461.
Cartan, H.: Quotient d'un espace analytique par un groupe d'automorphismes, In: Algebraic geometry and topology in honour of Lefschetz, 90–102, Princeton Univ. Press, Princeton, 1957.
Corlette, K.: Flat G-bundles with canonical metrics, J. Diff. Geom. 28 (1988), 361–382.
Doi, H.: Stable principal bundles on a projective plane, Sûrikenkôkyûroku, (1988), 132–147. (in Japanese)
Donaldson, D.K.: Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc., 55 (1987), 127–131.
Fujiki, A.: Closedness of the Douady spaces of compact Kähler spaces, Publ. RIMS, Kyoto Univ., 14 (1978), 1–52.
—: On the Douady space of a compact complex space in the category C, II, Publ. RIMS, Kyoto Univ., 20 (1984), 461–189.
—: On the de Rham cohomology group of a compact symplectic Kähler manifold, Adcanced Studies in Pure Math., 10 (1987), 105–165.
—: Stability and Hermitian-Einstein connection on a principal Higgs bundle on a compact Kähler manifold, in preparation.
Freed, D.S., and Uhlenbeck, K.K.: Instantons and four-manifolds, MSRI Publ. Springer, 1984.
Goldman, W.M.: The symplectic nature of fundamental group of surfaces, Advance in Math., 54 (1984), 200–225.
Goldman, W.M., and Millson, J.J.: The deformation theory of representations of fundamental groups of compact Kähler manifolds, Publ. Math. IHES, 67 (1988), 43–78.
Griffiths, P.A.: Extension problem in complex analysis I, In: Proc. Conf. on Complex Analysis, 113–142, Minneapolis 1964, Springer, 1965.
Griffiths, P.A.: Extension problem in complex analysis II, Amer. J. Math., 88 (1966), 306–446.
Guillemin, V., and Sternberg, S.: Geometric quantization and multiplicities of group representations, Invent. math., 67 (1982), 515–538.
Hitchin, N.J.: The self-duality equations on a surface, Proc. London Math. Soc., 55 (1987), 59–126.
—: Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91–114.
Hithcin, N.J., Karlhede, A., Lindström, U. and Rocek, M.: Hyperkähler metrics and supersymmetry, Commun. Math. Phys., 108 (1987), 535–589.
Johnson, D., and Millson, J.J.: Deformation spaces associated to compact hyperbolic manifolds, 48–105, In: discrete groups in geometry and analysis, Papers in Honor of G.D. Mostow, Progress in Math., 67, 1986, Birkhäuser.
Jost, J., and Yau, S.-T.: Harmonic maps and group representations in complex geometry, Lecture at Conf. in Kyoto, 1989.
Kirwan, F.C.: Cohomology of quotients in symplectic and algebraic geometry, Math. Notes 31, Princeton Univ. Press, 1984.
Kobayashi, S.: Differential geometry of complex vector bundles, Publ. Math. Soc. Japan 15, Iwanami and Princeton Univ. Press, 1987.
Kobayashi, S., and Nomizu, K.: Foundations of differential geometry, vol. 2, Wiley-Interscience, 1969.
Mehta, V.B., and Ramanathan, A.: Restriction of stable sheaves and representations of the fundamental group, Invent. math., 77 (1984), 163–172.
Mumford, D.: Geometric invariant theory, Springer Verlag, Berlin-Heidelberg-New York, 1965.
Palais, R.S.: Foundations in global nonlinear analysis, W.A. Benjamin, Inc., 1968.
Ramanathan, A., Stable principal bundles on a compact Riemann surfaces, Math. Ann., 213 (1975), 129–152.
Ramanan, S., and Ramanathan, A.: Some remarks on the instbility flag, Tohoku Math. J., 36 (1984), 269–281.
Ramanathan, A., and Subramanian, S.: Einstein-Hermitian connections on principal bundles and stability, J. reine angew. Math., 390 (1988), 21–31.
Simpson, C.T.: Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. of AMS, 1 (1988), 867–918.
—: Higgs bundles and local systems, preprint.
—: Moduli of representations of the fundamental group of a smooth projective variety, preprint.
Uhlenbeck, K., and Yau, S.-T.: On the existence of Hermitian-Yang-Mills connections on stable vector bundles, Comm. Pure and Appl. Math., 39 (1986), 257–293.
Weil, A.: Variétés kählériennes, nouvelle édition, Hermann, Paris, 1971.
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Fujiki, A. (1991). Hyperkähler structure on the moduli space of flat bundles. In: Noguchi, J., Ohsawa, T. (eds) Prospects in Complex Geometry. Lecture Notes in Mathematics, vol 1468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086187
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DOI: https://doi.org/10.1007/BFb0086187
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