Abstract
Using the Schottky uniformization of a marked Riemann surface, the space of equivalence classes of complex projective structures on a compact oriented C ∞ surface gets identified, in an obvious fashion, with the total space of the holomorphic cotangent bundle of the corresponding Teichmüller space. This identification is proved to be compatible with the natural symplectic structures on these two spaces. If we consider the other identification of the same two spaces obtained using the Bers’ construction of universal Riemann surface, then the compatibility of the symplectic structures was established by Kawai [S. Kawai, Math. Ann. 305 (1996) 161–182].
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