A support theorem for the X-ray transform on manifolds with plane covers

Abstract

This article is concerned with support theorems of the X-ray transform on non-compact manifolds with conjugate points. In particular, we prove that all simply connected 2-step nilpotent Lie groups have a support theorem. Important ingredients of the proof are the concept of plane covers and a support theorem for simple manifolds by Krishnan.We also provide examples of non-homogeneous 3-dimensional simply connected manifolds with conjugate points which have support theorems.

1 figure

References in corpus (4)

• Tensor tomography on Cartan-Hadamard manifolds
• On Radon transforms on compact Lie groups
• On the kernel of the maximal flat Radon transform on symmetric spaces of compact type
• The X-ray transform on 2-step nilpotent Lie groups of higher rank