Triple M-brane configurations and preserved supersymmetries

We investigate all standard triple composite M-brane intersections defined on products of Ricci-flat manifolds for preserving supersymmetries in eleven-dimensional N =1 supergravity. The explicit formulae for computing the numbers of preserved supersymmetries are obtained, which generalize the relations for topologically trivial flat factor spaces presented in the classification by Bergshoeff et al. We obtain certain examples of configurations preserving some fractions of supersymmetries, e.g. containing such factor spaces as K3, C^2_{*}/Z_2, a four-dimensional pp-wave manifold and the two-dimensional pseudo-Euclidean manifold R^{1,1}_{*}/Z_2.