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.
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页码：713 / 720
页数：8
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