most citedHigh curvature means low-rank: On the sectional curvature of Grassmann and Stiefel manifolds and the underlying matrix trace inequalities

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math.DG2025

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 Hü…

math.DG2024

The injectivity radius of the compact Stiefel manifold under the Euclidean metric

Ralf Zimmermann, Jakob Stoye

The injectivity radius of a manifold is an important quantity, both from a theoretical point of view and in terms of numerical applications. It is the largest possible radius withi…