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We study an inverse problem of determining a time-dependent potentialappearing in the wave equation in conformally transversally anisotropicmanifolds of dimension three or higher. These are compact Riemannian manifoldswith boundary that are conformally embedded in a product of the real line and atransversal manifold. Under the assumption of the attenuated geodesic raytransform being injective on the transversal manifold, we prove the uniquedetermination of time-dependent potentials from the knowledge of a certainpartial Cauchy data set.

Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds