The effect of the curvature of the carbon lattice is discussed taking into account NMR data on various fluorinated carbons including C₆₀ 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 °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 ¹⁹F → ¹³C cross polarization wide-line separation and inverse ¹⁹F → ¹³C cross polarization were also used for fluorinated C₆₀.