Ok Dantas I got it. When I exported from Cinema4D to an obj file, I exported it as only one objet when there were 5 meshes. If I export it as a 3ds format, all the meshes are separated and I can affect the textures to each mesh correctly.
I was not able to import 3ds format with Carrara until the new 6,2 updater. Now I can and that solved the problem.
Your idea of the UV map gave me the answer.
Thank you so much
Michel