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arXiv · 1801.06472

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

Norbert Peyerimhoff·Evangelia Samiou
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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.

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Norbert Peyerimhoff, Evangelia Samiou. 2018-01-19. A support theorem for the X-ray transform on manifolds with plane covers. https://doi.org/10.1017/s0305004119000148

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