  We investigate the Kosterlitz-Thouless transition for hexatic order on a free
fluctuating membrane and derive both a Coulomb gas and a sine-Gordon
Hamiltonian to describe it. In the former, both disclinations and Gaussian
curvature contribute to the charge density. In the latter, there is a linear
coupling between a scalar field and the Gaussian curvature. We derive
renormalization group recursion relations that predict a transition with
decreasing bending rigidity $\kappa$. Using the sine-Gordon model, we show that
there is no KT transition on a deformable sphere.
