# The ultimate upper bound on the injectivity radius of the Stiefel manifold

arXiv: https://arxiv.org/abs/2403.02079 · HTML: https://mlsanity.com/paper/2403.02079/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics](https://mlsanity.com/paper/2408.07072/) (2024)

## Abstract (arXiv)

We exhibit conjugate points on the Stiefel manifold endowed with any member of the family of Riemannian metrics introduced by H"uper et al. (2021). 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.