Work

The Ultimate Upper Bound on the Injectivity Radius of the Stiefel Manifold

Year: 2025

Type: article

Abstract: . We exhibit conjugate points on the Stiefel manifold endowed with any member of the family of Riemannian metrics introduced by Hüper et al. [ J. Geom. Mech., 13 (2021), pp. 55–72]. This family contains the well-known canonical and Euclidean metrics. An upper bound on the injectivity radius of the Stiefel manifold in the considered metric is then obtained as the minimum between the length of the geodesic along which the points are conjugate and the length of certain geodesic loops. Numerical experiments support the conjecture that the obtained upper bound is in fact equal to the injectivity radius.

Source: SIAM Journal on Matrix Analysis and Applications

DOI: 10.1137/24m1644808

Authors: P.-A. Absil, Simon Mataigne

Institution: UCLouvain

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Fonds De La Recherche Scientifique - FNRS

Award: G3420857747