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Projective structures with discrete holonomy representations

Name: Projective structures with discrete holonomy representations
Keywords: Mathematics - Differential Geometry, Differential Geometry (math.DG), Riemann surface, Mathematics - Complex Variables, FOS: Mathematics, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Compact Riemann surfaces and uniformization, holonomy representation, Teichmüller spaces, Complex Variables (math.CV)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 1999Embargo end date: 01 Jan 1995Publisher:American Mathematical Society (AMS)Journal:Transactions of the American Mathematical Society, volume 351, pages 813-823 (issn: 0002-9947, eissn: 1088-6850,

Authors: Hiroshige Shiga; Harumi Tanigawa;

doi: 10.1090/s0002-9947-99-02043-7 , 10.48550/arxiv.math/9508214

arXiv: http://arxiv.org/abs/math/9508214

Projective structures with discrete holonomy representations

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Abstract

Let $K(X)$ denote the set of projective structures on a compact Riemann surface $X$ whose holonomy representations are discrete. We will show that each component of the interior of $K(X)$ is holomorphically equivalent to a complex submanifold of the product of Teichm��ller spaces and the holonomy representation of every projective structure in the interior of $K(X)$ is a quasifuchsian group.

Related Organizations

Institute of Science Tokyo
Japan
Nagoya University
Japan

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), Riemann surface, Mathematics - Complex Variables, FOS: Mathematics, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Compact Riemann surfaces and uniformization, holonomy representation, Teichmüller spaces, Complex Variables (math.CV)

5 Research products, page 1 of 1

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