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Ray Transform of Symmetric Tensor Fields for a Spherically Symmetric Metric

  • V. A. Sharafutdinov

Abstract

The ray transform I on a Riemannian manifold (M, g) with boundary is the linear operator on the space of symmetric tensor fields of degree m that sends a tensor field into the set of its integrals over all maximal geodesics. The principal question on the ray transform is formulated as follows: for what Riemannian manifolds and values of m does the kernel of I coincide with the space of potential fields? A tensor m-field f is called potential if it is the symmetric part of the covariant derivative of another tensor field of degree m - 1. The conjecture is proved in the case when M is the ball in Euclidean space and the metric g is spherically symmetric.

Keywords

Riemannian Manifold Fourier Series Covariant Derivative Potential Field Fourier Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • V. A. Sharafutdinov
    • 1
  1. 1.Institute of MathematicsRussian Academy of SciencesNovosibirskRussia

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