Invariant distributions and the geodesic ray transform

Abstract

We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $m$-tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over the set of solenoidal $m$-tensors. We work with compact simple manifolds, but several of our results apply to non-trapping manifolds with strictly convex boundary.

27 pages; final version, to appear in Analysis & PDE

References in corpus (2)

• The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta
• Invariant distributions, Beurling transforms and tensor tomography in higher dimensions

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