Projective structures with discrete holonomy representations

Shiga, Hiroshige; Tanigawa, Harumi

doi:10.1090/S0002-9947-99-02043-7

Projective structures with discrete holonomy representations
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by Hiroshige Shiga and Harumi Tanigawa

Trans. Amer. Math. Soc. 351 (1999), 813-823

DOI: https://doi.org/10.1090/S0002-9947-99-02043-7

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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 Teichmüller spaces and the holonomy representation of every projective structure in the interior of $K(X)$ is a quasifuchsian group.

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