Shortest geodesic loops, sectional curvature, and injectivity radius of the Stiefel manifold

Stoye, Jakob;Mataigne, Simon;Absil, Pierre-Antoine;Zimmermann, Ralf
(2026) BIT Numerical Mathematics — Vol. 66, n° 3, p. 1-43 (2026)

Files

2511.01563v1.pdf
  • Open Access
  • Adobe PDF
  • 777.34 KB
Download

Details

Authors
Abstract
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 Hüper et al. (2021). This family includes, in particular, the canonical and Euclidean metrics. By combining existing and new bounds on the sectional curvature, we determine the exact value of the injectivity radius of the Stiefel manifold under a wide range of members of the metric family.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Stoye, J., Mataigne, S., Absil, P.-A., & Zimmermann, R. (2026). Shortest geodesic loops, sectional curvature, and injectivity radius of the Stiefel manifold. BIT Numerical Mathematics, 66(3), 1-43. https://doi.org/10.1007/s10543-026-01141-9 (Original work published 2026)