  We prove that a potential $q$ can be reconstructed from the
Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g + q$ in a
fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that
an admissible metric $g$ in a fixed conformal class can be constructed from the
Dirichlet-to-Neumann map for $\Delta_g$. This is a constructive version of
earlier uniqueness results by Dos Santos Ferreira et al. on admissible
manifolds, and extends the reconstruction procedure of Nachman in Euclidean
space. The main points are the derivation of a boundary integral equation
characterizing the boundary values of complex geometrical optics solutions, and
the development of associated layer potentials adapted to a cylindrical
geometry.
