In recent years, several attempts have been made to characterize the geometric structure of fullerenes by means of topological shape factors in order to predict their physical properties and stability. In this paper, we present a simple method to estimate the stability of fullerenes on the basis of quantitative topological criteria. This approach is based on the concept of the generalized combinatorial curvatures defined on the set of simple graphs embedded on a closed surface without boundary (sphere, torus, projective plane, Klein bottle). It is shown that starting with the computed generalized combinatorial curvatures several novel topological indices can be generated. From computations performed on a set of C40 and C60 fullerenes, we concluded that the four topological shape factors tested (Λ(-1), (-1), Λ(1) and (1)) could be successfully used to preselect the most stable fullerene isomers.