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We consider the hyperkähler extension of Teichmüller space with the Weil-Petersson metric. We describe its recent construction as a hyperkähler quotient and examine the defining equations for the resulting moduli space. We examine relations between this moduli space and the quasi-Fuchsian deformation space of the surface, with particular attention to the connection with the canonical holomorphic symplectic structure. We also consider the connection with Taubes moduli space of hyperbolic germs and whether it is possible to extend the hyperkähler structure in any fashion.