Ray Transform of Symmetric Tensor Fields for a Spherically Symmetric Metric

  • V. A. Sharafutdinov


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.


Riemannian Manifold Fourier Series Covariant Derivative Potential Field Fourier Coefficient 
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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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