Superstring vacua are normally presumed to be of the form M×K, where dim(M)=4, dim(K)=6, and where × denotes the global Riemannian product. Since, however, one would ultimately wish to understand the external/internal distinction in terms of some dynamical mechanism (‘‘spontaneous splitting’’) involving vacuum expectation values of local fields, it may be preferable to use a local Riemannian product at the outset. Here it is shown that these spaces, which have the same local (block-diagonal) type of metric as M×K, can be described and classified by examining the isometry groups of the Calabi–Yau manifolds which have been proposed as models for the internal superstring vacua.