The range of the Radon transform on the real hyperbolic Grassmann manifold

Let Γ n k be the space of all the k-dimensional totally geodesic submanifolds of the n-dimensional real hyperbolic space where 1 ≤ k ≤ n − 1. We prove that the Radon transform R for double fibrations of the real hyperbolic Grassmann manifolds Γ n p and Γ n q with respect to the inclusion incidence r...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerző: Ishikawa Satoshi
Dokumentumtípus: Cikk
Megjelent: 2020
Sorozat:Acta scientiarum mathematicarum
Kulcsszavak:Matematika
Tárgyszavak:
doi:10.14232/actasm-019-773-1

Online Access:http://acta.bibl.u-szeged.hu/69370
Leíró adatok
Tartalmi kivonat:Let Γ n k be the space of all the k-dimensional totally geodesic submanifolds of the n-dimensional real hyperbolic space where 1 ≤ k ≤ n − 1. We prove that the Radon transform R for double fibrations of the real hyperbolic Grassmann manifolds Γ n p and Γ n q with respect to the inclusion incidence relations maps C ∞0 (Γn p ) bijectively onto the space of all the functions in C ∞0 (Γn q ) which satisfy a certain system of linear partial differential equations explicitly constructed from the left infinitesimal action of the transformation group when 0 ≤ p < q ≤ n − 1 and dim Γ n p < dim Γ n q . Our approach is based on the generalized method of gnomonic projections. We also treat the dual Radon transform R.
Terjedelem/Fizikai jellemzők:225-264
ISSN:2064-8316