Shortest Geodesic Loops, Sectional Curvature, and Injectivity Radius of the Stiefel Manifold
Jakob Stoye, Simon Mataigne, P.-A. Absil, Ralf Zimmermann
我们确定Stiefel流形上最短的非平凡大地测量回路的长度,该流形具有Hüper等人介绍的黎曼指标单参数家族的任何成员。 (2021年)。 这个家庭特别包括规范和欧几里德指标。 通过在节段曲率上结合现有和新边界,我们确定在公制家族的广泛成员下Stiefel流形的注射半径的确切值。
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.