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

Peyerimhoff, Norbert; Samiou, Evangelia

doi:10.1017/s0305004119000148

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

Peyerimhoff, Norbert; Samiou, Evangelia

Authors

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

Evangelia Samiou

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

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This article has been published in a revised form in Mathematical proceedings of the Cambridge Philosophical Society https://doi.org/10.1017/S0305004119000148. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge Philosophical Society.