Kähler geometry of the universal Teichmüller space and coadjoint orbits of the Virasoro group
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The Kähler geometry of the universal Teichmüller space and related infinite-dimensional Kähler manifolds is studied. The universal Teichmüller space T may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The classical Teichmüller spaces T(G), where G is a Fuchsian group, are contained in T as complex Kähler submanifolds. The homogeneous spaces Diff+(S 1)/Möb(S 1) and Diff+(S 1)/S 1 of the diffeomorphism group Diff+(S 1) of the unit circle are closely related to T. They are Kähler Frechet manifolds that can be realized as coadjoint orbits of the Virasoro group (and exhaust all coadjoint orbits of this group that have the Kähler structure).
KeywordsSTEKLOV Institute Symplectic Form Fuchsian Group Coadjoint Orbit Beltrami Equation
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- 1.L. V. Ahlfors, Lectures on Quasiconformal Mappings (Van Nostrand, Princeton, 1966; Mir, Moscow, 1969).Google Scholar
- 2.R. Bowen, “Hausdorff Dimension of Quasicircles,” Publ. Math., Inst. Hautes Étud. Sci. 50, 259–273 (1979).Google Scholar
- 6.A. A. Kirillov, “Infinite Dimensional Lie Groups: Their Orbits, Invariants and Representations. The Geometry of Moments,” in Twistor Geometry and Nonlinear Systems, Primorsko (Bulg.), 1980 (Springer, Berlin, 1982), Lect. Notes Math. 970, pp. 101–123.Google Scholar
- 10.S. Nag, The Complex Analytic Theory of Teichmüller Spaces (J. Wiley and Sons, New York, 1988).Google Scholar
- 15.A. Pressley and G. Segal, Loop Groups (Clarendon Press, Oxford, 1986; Mir, Moscow, 1990).Google Scholar
- 17.A. G. Sergeev, Kähler Geometry of Loop Spaces (Moscow Cent. Cont. Math. Educ., Moscow, 2001) [in Russian].Google Scholar