X-RAY TRANSFORM ON DAMEK-RICCI SPACES

被引：6

作者：

Rouviere, Francois ^{[1
]}

机构：

[1] Univ Nice, Lab JA Dieudonne, F-06108 Nice 2, France

来源：

INVERSE PROBLEMS AND IMAGING | 2010年 / 4卷 / 04期

关键词：

Damek-Ricci space; hyperbolic space; X-ray transform; totally geodesic submanifold;

D O I：

10.3934/ipi.2010.4.713

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Damek-Ricci spaces, also called harmonic NA groups, make up a large class of harmonic Riemannian manifolds including all hyperbolic spaces. We prove here an inversion formula and a support theorem for the X-ray transform, i.e. integration along geodesics, on those spaces. Using suitably chosen totally geodesic submanifolds we reduce the problems to similar questions on low-dimensional hyperbolic spaces.

引用

页码：713 / 720

页数：8

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