Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature

Let [Formula: see text] be a sequence of non-collapsed [Formula: see text]-manifolds with two-sidedly bounded Ricci curvature. We show that the Gromov-Haudorff limit space, [Formula: see text], of the associated sequence of orthonormal frame bundles, [Formula: see text], 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 [Formula: see text] whose complement contains an open and dense [Formula: see text]-Riemannian manifold.