Titlebook: Integral Geometry and Radon Transforms; Sigurdur Helgason Textbook 2010 Sigurdur Helgason 2010 Homogeneous spaces in duality.Manifolds and

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The Radon Transform on Two-Point Homogeneous Spaces,Let . be a complete Riemannian manifold, . a point in . and .. the tangent space to . at .. Let Exp. denote the mapping of .. into . given by Exp.(.) = g.(1), where t → g.(.) is the geodesic in . through . with tangent vector . at . = g.(0).

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The X-Ray Transform on a Symmetric Space,The X-ray transform which we studied for R. of course makes sense for an arbitrary complete Riemannian manifold ..

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Symmetric Spaces,Since Cartan’s symmetric spaces have entered in some chapters of this book we give here a short description of the basics of their theory but with some proofs omitted. Detailed proofs can be found in my book [1978].

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d chapters with bibliographical notes, exercises, and furtheIn this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fu