Tensor tomography on Cartan–Hadamard manifolds. (16th March 2018)

• Record Type: Journal Article
• Authors: Lehtonen, Jere; Railo, Jesse; Salo, Mikko
• Is Part Of: Inverse problems. Volume 34:Number 4(2018:Apr.)
• Publication Date: 2018-03-16
• Subjects: differential geometry -- tensor tomography -- Cartan–Hadamard manifolds -- x-ray transform; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaaf85
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We 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 arXiv:1612.04800) to dimensions n ⩾ 3 and to the case of tensor fields of any order.