Geodesic
The Inversion of the X-ray Transform on a Compact Symmetric Space
Journal of Lie theory, Tome 17 (2007) no. 2, pp. 307-315.

Voir la notice de l'article provenant de la source Heldermann Verlag

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].
Classification : 22E30, 43A85, 44A12, 53C65, 22E46, 53C35
Mots-clés : Compact symmetric spaces, Funk transform, Radon transform, X-ray transform 
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S. Helgason . The Inversion of the X-ray Transform on a Compact Symmetric Space. Journal of Lie theory, Tome 17 (2007) no. 2, pp. 307-315. http://geodesic.mathdoc.fr/item/JLT_2007_17_2_JLT_2007_17_2_a4/