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Journal of Lie Theory 17 (2007), No. 2, 307--315
Copyright Heldermann Verlag 2007

The Inversion of the X-ray Transform on a Compact Symmetric Space

Sigurdur Helgason
Dept. of Mathematics, Massachusetts Inst. of Technology, Cambridge, MA 02139, U.S.A.

The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M, proved in a previous paper of the author ["Totally geodesic spheres in compact symmetric spaces", Math. Ann. 165 (1966), 309--317].

Keywords: Compact symmetric spaces, Funk transform, Radon transform, X-ray transform.

MSC: 22E30, 43A85, 44A12, 53C65; 22E46, 53C35

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