English

Tensor tomography on Cartan-Hadamard manifolds

Differential Geometry 2019-09-06 v2

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 n3n \geq 3 and to the case of tensor fields of any order.

Keywords

Cite

@article{arxiv.1705.10126,
  title  = {Tensor tomography on Cartan-Hadamard manifolds},
  author = {Jere Lehtonen and Jesse Railo and Mikko Salo},
  journal= {arXiv preprint arXiv:1705.10126},
  year   = {2019}
}

Comments

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