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We show that a tensor field of any rank integrates to zero over all brokenrays if and only if it is a symmetrized covariant derivative of a lower ordertensor which satisfies a symmetry condition at the reflecting part of theboundary and vanishes on the rest. This is done in a geometry with non-positivesectional curvature and a strictly convex obstacle in any dimension. We givetwo proofs, both of which contain new features also in the absence ofreflections. The result is new even for scalars in dimensions above two.

Broken ray tensor tomography with one reflecting obstacle