  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.
