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We consider the inverse problem of recovering a potential from the Dirichletto Neumann map at a large fixed frequency on certain Riemannian manifolds. Weextend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to thecase of simple manifolds, and more generally to manifolds where the geodesicray transform is stably invertible. The argument involves an invariantlyformulated construction of Gaussian beam quasimodes with uniform bounds for theunderlying constants.

The anisotropic Calder\'on problem at large fixed frequency on manifolds with invertible ray transform