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

Key Points

• The research addresses the characteristics of Gromov-Hausdorff limit spaces derived from orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature.
• Investigated a sequence of non-collapsed manifolds with two-sidedly bounded Ricci curvature.
• Analyzed the Gromov-Hausdorff limit space of the associated orthonormal frame bundles.
• Studied the singular set and its complement in relation to the Ricci limit space.
• The singular set of the limit space has codimension consistent with that of Ricci limit spaces.
• The complement of the singular set contains an open and dense Riemannian manifold.

Abstract