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

BIT Numerical Mathematics 2026 Book chapter Open access

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Authors: Jakob Stoye, Simon Mataigne, P. -A. Absil, Ralf Zimmermann
DOI: 10.1007/s10543-026-01141-9
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Morphological variations and asymmetry Geometric Analysis and Curvature Flows Advanced Differential Geometry Research

Publication details

Journal / source
BIT Numerical Mathematics
Volume
66
Issue
3
Publication date
22 June 2026
Language
EN
Document type
Book chapter