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.
Si et al. (Fri,) studied this question.