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Conformally St{\"a}ckel manifolds can be characterized as the class ofn-dimensional pseudo-Riemannian manifolds (M, G) on which the Hamilton-Jacobiequation G($\nabla$u, $\nabla$u) = 0 for null geodesics and the Laplaceequation --$\Delta$ G $\psi$ = 0 are solvable by R-separation of variables. Inthe particular case in which the metric has Riemannian signature, they provideexplicit examples of metrics admitting a set of n--1 commuting conformalsymmetry operators for the Laplace-Beltrami operator $\Delta$ G. In this paper,we solve the anisotropic Calder{\'o}n problem on compact 3-dimensionalRiemannian manifolds with boundary which are conformally St{\"a}ckel, that iswe show that the metric of such manifolds is uniquely determined by theDirichlet-to-Neumann map measured on the boundary of the manifold, up todieomorphims that preserve the boundary.

The anisotropic Calder{\'o}n problem on 3-dimensional conformally St{\"a}ckel manifolds