Hitchin, Nigel J. Metrics on moduli spaces. (English) Zbl 0618.32017 Algebraic geometry, Proc. Lefschetz Centen. Conf., Mexico City/Mex. 1984, Pt. I, Contemp. Math. 58, 157-178 (1986). [For the entire collection see Zbl 0588.00015.] The main result of this paper is the observation due to the author: ”A hyper-Kähler metric is shown to exist on an open set of the moduli space of all flat bundles on a Riemann surface. The moduli space of irreducible unitary connections together with its natural metric is the fixed point set of a circle action in this space”. Reviewer: P.Cherenack Cited in 7 Documents MSC: 32G13 Complex-analytic moduli problems 14D20 Algebraic moduli problems, moduli of vector bundles 53B35 Local differential geometry of Hermitian and Kählerian structures 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) 32L25 Twistor theory, double fibrations (complex-analytic aspects) 53C80 Applications of global differential geometry to the sciences Keywords:vortices; vector bundles; twistors; hyper-Kähler metric; moduli space; unitary connections Citations:Zbl 0588.00015 PDFBibTeX XML