X-ray transform on Damek-Ricci spaces
François Rouvière
Inverse Problems & Imaging 2010, 4(4): 713-720 doi: 10.3934/ipi.2010.4.713
Damek-Ricci spaces, also called harmonic $NA$ groups, make up a large class of harmonic Riemannian manifolds including all hyperbolic spaces. We prove here an inversion formula and a support theorem for the X-ray transform, i.e. integration along geodesics, on those spaces.
   Using suitably chosen totally geodesic submanifolds we reduce the problems to similar questions on low-dimensional hyperbolic spaces.
keywords: hyperbolic space totally geodesic submanifold. Damek-Ricci space X-ray transform

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