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

Jakob Stoye; Simon Mataigne; P. A. Absil; Ralf Zimmermann

doi:10.1007/s10543-026-01141-9

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

Jakob Stoye^*
, Simon Mataigne
, P. A. Absil
, Ralf Zimmermann

^*Corresponding author for this work

Braunschweig University of Technology
Catholic University of Louvain

Research output: Contribution to journal › Journal article › Research › peer-review

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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.

Original language	English
Article number	42
Journal	BIT Numerical Mathematics
Volume	66
Issue number	3
Number of pages	43
ISSN	0006-3835
DOIs	https://doi.org/10.1007/s10543-026-01141-9
Publication status	Published - Sept 2026

Keywords

geodesic loops
injectivity radius
sectional curvature
Stiefel manifold

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10.1007/s10543-026-01141-9Licence: CC BY

Open Access VersionFinal published version, 724 KBLicence: CC BY

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AU - Stoye, Jakob

AU - Mataigne, Simon

AU - Absil, P. A.

AU - Zimmermann, Ralf

PY - 2026/9

Y1 - 2026/9

N2 - 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.

AB - 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.

KW - geodesic loops

KW - injectivity radius

KW - sectional curvature

KW - Stiefel manifold

U2 - 10.1007/s10543-026-01141-9

DO - 10.1007/s10543-026-01141-9

M3 - Journal article

AN - SCOPUS:105042472459

SN - 0006-3835

VL - 66

JO - BIT Numerical Mathematics

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

Abstract

Keywords

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