#### Vol. 9, No. 8, 2016

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Invariant distributions and the geodesic ray transform

### Gabriel P. Paternain and Hanming Zhou

Vol. 9 (2016), No. 8, 1903–1930
##### 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 nontrapping manifolds with strictly convex boundary.

##### Keywords
geodesic ray transform, first integral, tensor tomography, invariant distribution
Primary: 53C65
Secondary: 58J40