Abstract
We define the Teichmüller pseudodistance on the space of spherical CR structures on a fixed compact manifold by using quasiconformal mappings between spherical CR manifolds. The pseudodistance is shown to be a complete distance.
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Izeki H. The Teichmüller distance on the space of flat conformal structures. Conform Geom Dyn, 1998, 2: 1–24
Pansu P. Métriques de Carnot-Caratheodory et quasiisométries de espaces symétriques de rang un. Ann Math, 1989, 129: 1–60
Wang W. Representations of SU(p,q) and CR geometry I. Journal of Mathematics of Kyoto University, 2005, 45(4): 759–780
Chern S S, Moser J. Real hypersurfaces in complex manifolds. Acta Math, 1974, 133: 219–271
Burns D, Shnider S. Spherical hypersurfaces in complex manifolds. Invent Math, 1976, 33: 223–246
Kamishima Y, Tsuboi T. CR-structures on Seifert manifolds. Invent Math, 1991, 104: 149–163
Wang W. Canonical contact forms on spherical CR manifolds. Journal of Euripean Mathematical Society, 2003, 5: 245–273
Choi S. Geometric structures on orbifolds and holonomy representations. Geom Dedicata, 2004, 104: 161–199
Thurston W. The geometry and topology of 3-Manifolds. Lecture Notes, Princeton: Princeton Univ Press, 1980
Canary R, Epstein D, Green P. Notes on notes of Thurston. In: Analytical and Geometric Aspects of Hyperbolic Space. London Math Soc Lecture Note Ser 111, Cambridge: Cambridge Univ Press, 1987, 3–92
Goldman W, Millson J. Local rigidity of discrete groups acting on complex hyperbolic space. Invent Math, 1987, 88(3): 495–520
Humphreys J. Linear algebraic groups. Graduate Texts in Mathematics 21. New York-Heidelberg: Springer-Verlag, 1975
Whitney H. Elementary structure of real algebraic varieties. Ann of Math, 1957, 66(2): 545–556
Korányi A, Reimann H. Foundations for the theory of quasiconformal mappings on the Heisenberg group. Adv Math, 1995, 111(1): 1–87
Dairbekov N. Stability of mappings with bounded distortion on the Heisenberg group. Sibirsk Mat Zh, 2002, 43(2): 281–294
Gromov M. Carnot-Carathéodory spaces seen from within. In: Sub-Riemannian Geometry, Progr Math, Basel: Birkhäuser, 1996, 79–323
Gray J. Some global properties of contact structures. Ann Math, 1959, 69(2): 421–450
Martinet J. Formes de contact sur les variétés de dimension 3. Lecture Notes in Math, 209, Berlin: Springer, 1971, 142–163
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Dedicated to Professor Sheng GONG on the occasion of his 75th birthday
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Wang, W. The Teichmüller distance on the space of spherical CR structures. SCI CHINA SER A 49, 1523–1538 (2006). https://doi.org/10.1007/s11425-006-2052-y
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DOI: https://doi.org/10.1007/s11425-006-2052-y