Gromov-Hausdorff Limit of Orthonormal Frame Bundles of Non-Collapsed Manifolds with Bounded Ricci Curvature

Let M-i be a sequence of non-collapsed n-manifolds with two-sidedly bounded Ricci curvature. We show that the Gromov-Hausdorff limit space, Y, of the associated sequence of orthonormal frame bundles, FMi, equipped with an almost canonical metric, shares similar properties as a Ricci limit space of non-collapsing sequence i.e. the singular set has codimension >= 4 whose complement contains an open and dense C-1,C-alpha-Riemannian manifold.