Sub-Riemannian geometry of Stiefel manifolds

2013/05/26 by Christian Autenried, Autenried, Christian, Irina Markina +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1305.6056

openalex publication_date 2013/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we consider the Stiefel manifold V_n;k as a principal U(k)- bundle over the Grassmann manifold and study the cut locus from the unit element. We gave the complete description of this cut locus on V_n;1 and presented the sufficient condition on the general case. At the end, we study the complement to the cut locus of V_2k;k.

Citations

• Curvatures of left invariant metrics on lie groups
• Shortest paths for sub-Riemannian metrics on rank-two distributions

Related

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• Some Observations on projective Stiefel Manifolds
• On the Injectivity Radius of the Stiefel Manifold: Numerical investigations and an explicit construction of a cut point at short distance
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