PROJECTIVE STRUCTURES WITH

DISCRETE HOLONOMY REPRESENTATIONS

Hiroshige Shiga and Harumi Tanigawa

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.

Typeset by AMS-TEX