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

Peyerimhoff, Norbert; Samiou, Evangelia

Abstract

This paper 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.

Citation

Peyerimhoff, N., & Samiou, E. (2020). A support theorem for the X-ray transform on manifolds with plane covers. Mathematical Proceedings of the Cambridge Philosophical Society, 169(1), 149-158. https://doi.org/10.1017/s0305004119000148

• Journal Article Type: Article
• Acceptance Date: Feb 18, 2019
• Online Publication Date: Apr 25, 2019
• Publication Date: 2020-07
• Deposit Date: Mar 6, 2019
• Publicly Available Date: Oct 25, 2019
• Journal: Mathematical Proceedings of the Cambridge Philosophical Society
• Print ISSN: 0305-0041
• Electronic ISSN: 1469-8064
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 169
• Issue: 1
• Pages: 149-158
• DOI: https://doi.org/10.1017/s0305004119000148
• Public URL: https://durham-repository.worktribe.com/output/1306837