Published Paper
Inserted: 3 aug 2026
Last Updated: 3 aug 2026
Journal: Rendiconti del Seminario Matematico della Università di Padova
Year: 2026
Doi: 10.4171/RSMUP/207
Abstract:
The Stiefel and Grassmann manifolds have been studied extensively and play a prominent role in many applications. Their geodesic structure is well understood; in particular, minimal geodesics and the cut locus in the Grassmann manifold admit classical descriptions. The oriented Grassmann manifold is less frequently treated explicitly. In this note we review the relevant Stiefel and Grassmann results for Hilbert spaces, including the infinite-dimensional case, give direct proofs adapted to our notation, and derive an explicit minimal-geodesic criterion and a cut-locus characterization for the oriented Grassmann manifold.
Keywords: stiefel manifold, hilbert space, grassmann manifold, cut locus, oriented Grassmann manifold, Riemannian geodesics, minimal geodesics, principal angles, singular value decomposition
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