The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds

Conformally Stäckel manifolds can be characterized as the class of $n$-dimensional pseudo-Riemannian $(M,G)$ on which Hamilton–Jacobi equation $$ G(\nabla u, \nabla u) = 0 for null geodesics and Laplace $-\Delta\_G , \psi 0$ are solvable by R-separation variables. In particular case in metric has Riemannian signature, they provide explicit examples metrics admitting a set $n-1$ commuting conformal symmetry operators Laplace–Beltrami operator $\Delta\_G$. this paper, we solve anisotropic Calderón problem compact $3$-dimensional with boundary conformally Stäckel, that is show such uniquely determined Dirichlet-to-Neumann map measured manifold, up to diffeomorphims preserve boundary.