Tensor tomography on Cartan-Hadamard manifolds

Abstract

We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016) to dimensions $n\ge 3$ and to the case of tensor fields of any order.

23 pages; accepted manuscript; new section 1.1 and references, theorems 1.1 and 1.2 now more precise

References in corpus (1)

• The X-ray transform for connections in negative curvature

Cited by in corpus (4)

• Broken ray transform for twisted geodesics on surfaces with a reflecting obstacle
• X-Ray Transform in Asymptotically Conic Spaces
• On mixed and transverse ray transforms on orientable surfaces
• A support theorem for the X-ray transform on manifolds with plane covers