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 H\"uper 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.

翻译：我们确定了在Hüper等人（2021）引入的单参数黎曼度量族中任意度量下Stiefel流形上非平凡最短测地线环的长度。该度量族特别包含典型度量与欧氏度量。通过结合现有及新推导的截面曲率界，我们确定了该度量族广泛成员下Stiefel流形单射半径的精确值。