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

Part of: Lie groups Integral transforms, operational calculus Global differential geometry

Published online by Cambridge University Press:  25 April 2019

NORBERT PEYERIMHOFF  and
EVANGELIA SAMIOU
NORBERT PEYERIMHOFF
Affiliation:
Department of Mathematical Sciences, Durham University, Science Laboratories South Road, Durham, DH1 3LE. e-mail: norbert.peyerimhoff@durham.ac.uk
EVANGELIA SAMIOU
Affiliation:
Department of Mathematics and Statistics, University of Cyprus P.O. Box 20537, 1678 Nicosia, Cyprus. e-mail: samiou@ucy.ac.cy
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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.

MSC classification

Primary: 53C65: Integral geometry 44A12: Radon transform
Secondary: 22E25: Nilpotent and solvable Lie groups
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 1 , July 2020 , pp. 149 - 158
Copyright
© Cambridge Philosophical Society 2019

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