INVERSE BOUNDARY PROBLEMS FOR BIHARMONIC OPERATORS IN TRANSVERSALLY ANISOTROPIC GEOMETRIES

We study inverse boundary problems for first order perturbations of the biharmonic operator on a conformally transversally anisotropic Riemannian manifold of dimension n \geq 3. We show that a continuous first order perturbation can be determined uniquely from the knowledge of the set of the Cauchy data on the boundary of the manifold provided that the geodesic X-ray transform on the transversal manifold is injective.