Ray Transform on Riemannian Manifolds

Vladimir A. Sharafutdinov
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Vladimir A. Sharafutdinov: Sobolev Institute of Mathematics

A chapter in New Analytic and Geometric Methods in Inverse Problems, 2004, pp 187-259 from Springer

Abstract: Abstract What is integral geometry? Since the famous paper by I. Radon in 1917, it has been agreed that integral geometry problems consist in determining sonic function or a more general object (cohomology class, tensor field, etc.) on a manifold, given its integrals over submanifolds of a prescribed class. In these lectures we only consider integral geometry problems for which the above-mentioned submanifolds are one-dimensional. Strictly speaking, the latter are always geodesics of a fixed Riemannian metric, in particular straight lines in Euclidean space. The exception is Lecture 1 in which we consider an arbitrary regular family of curves in a two-dimensional domain.

Keywords: Vector Field; Riemannian Manifold; Local Coordinate System; Tensor Field; Integral Geometry (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-662-08966-8_6

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