The effect of the curvature of the carbon lattice is discussed taking into account NMR data on various fluorinated carbons including C(60) fullerenes, single, double and multiwall carbon nanotubes. Graphite fluorides and highly fluorinated fullerenes are used as limit model compounds for planar and spherical geometries, respectively. The curvature results in a weakening of the C-F bonding covalence. First of all, various highly fluorinated fullerenes with increasing F/C molar ratio were prepared by treatment with pure gaseous fluorine. A preliminary study using XRD, EPR and IR spectroscopy confirms that the highest fluorination level can be reached either at 133 or at 300 degrees C. In order to extract the correlation between fluorine and carbon atoms and the C-F bond length, specific sequences such as solid echo, two-dimensional (19)F -->(13)C cross polarization wide-line separation and inverse (19)F -->(13)C cross polarization were also used for fluorinated C(60).