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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Projective structures
with discrete holonomy representations


Authors: Hiroshige Shiga and Harumi Tanigawa
Journal: Trans. Amer. Math. Soc. 351 (1999), 813-823
MSC (1991): Primary 32G15; Secondary 30F10
MathSciNet review: 1443890
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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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Additional Information

Hiroshige Shiga
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Tokyo 152 Japan
Email: shiga@math.titech.ac.jp

Harumi Tanigawa
Affiliation: Graduate School of Polymathematics, Nagoya University, Nagoya 464-01 Japan
Email: harumi@math.nagoya-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02043-7
PII: S 0002-9947(99)02043-7
Additional Notes: Research at MSRI is supported by NSF grant #DMS–9022140
Article copyright: © Copyright 1999 American Mathematical Society