Some basic aspects regarding the geometry of the interatomic surfaces of the theory of atoms in molecules are considered. After showing that the global Gauss-Bonnet theorem poses severe difficulties on the calculation of the total Gaussian curvatures of unbounded interatomic surfaces, we propose the use of the local value of the Gaussian curvature at the bond critical point as a better suited indicator of the geometry of the surfaces. To that end, we report analytical expressions for the curvatures of gradient lines and interatomic surfaces at critical points. (C) 2003 American Institute of Physics.