4 papers · 1 filter
Shortest Geodesic Loops, Sectional Curvature, and Injectivity Radius of the Stiefel Manifold
Jakob Stoye, Simon Mataigne, P. -A. Absil +1
We determine the length of the shortest nontrivial geodesic loops on the Stiefel manifold endowed with any member of the one-parameter family of Riemannian metrics introduced by HÃ…
On the approximation of the Riemannian barycenter
Simon Mataigne, P. -A. Absil, Nina Miolane
We present a method for computing an approximate Riemannian barycenter of a collection of points lying on a Riemannian manifold. Our approach relies on the use of theoretically pro…
The ultimate upper bound on the injectivity radius of the Stiefel manifold
P. -A. Absil, Simon Mataigne
We exhibit conjugate points on the Stiefel manifold endowed with any member of the family of Riemannian metrics introduced by Hüper et al. (2021). This family contains the well-kn…
Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, P. -A. Absil, Nina Miolane
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riem…