Support Theorems for Totally Geodesic Radon Transforms on Constant Curvature Spaces
نویسندگان
چکیده
منابع مشابه
On Splitting Theorems for Cat(0) Spaces and Compact Geodesic Spaces of Non-positive Curvature
In this paper, we prove some splitting theorems for CAT(0) spaces on which some product group acts geometrically and show a splitting theorem for compact geodesic spaces of nonpositive curvature. A CAT(0) group Γ is said to be rigid, if Γ determines the boundary up to homeomorphism of a CAT(0) space on which Γ acts geometrically. Croke and Kleiner have constructed a non-rigid CAT(0) group. As a...
متن کاملTotally geodesic submanifolds in Riemannian symmetric spaces
In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification of the totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2. To appear in the Proceedings volume for the conference V...
متن کاملClosures of Totally Geodesic Immersions in Manifolds of Constant Negative Curvature
Let 800(1, n) denote the connected component of the group of linear transformations of IRn+l preserving the bilinear form Abstract Using techniques of Lie groups and ergodic theory, it can be shown that in a compact manifold of constant negative curvature, the closure of a totally geodesic, complete (immersed) submanifold of dimension atleast 2 is a totally geodesicimmersed submanifold. The mai...
متن کاملSupport theorems for the Radon transform and Cramér-Wold theorems
This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distri...
متن کاملSupport Theorems for Horocycles on Hyperbolic Spaces
(i) An explicit description of the range D(X)̂where X is a Euclidean space or a symmetric space of the noncompact type ([2], [3]). Here (D = Cc ). In the first case, f̂ in (1.1) is integration over hyperplanes in X = Rn; in the latter case f̂ in (1.1) refers to integration over horocycles ξ in the symmetric space X. (ii) Medical application in X-ray reconstruction ([6], p.47). (iii) Existence theo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.2307/2161033