The content delves into geodesics and Jacobi fields on the Stiefel manifold, aiming to investigate cut points and conjugate points. Numerical experiments are conducted to assess the sharpness of the injectivity radius bound. Theoretical foundations and explicit examples are provided.
Reviewing key concepts such as geodesics, Jacobi fields, sectional curvature, and cut points on the Stiefel manifold. Investigating numerical experiments to evaluate if the injectivity radius bound is accurate. Exploring methods to determine cut points and conjugate points along geodesics. Providing an explicit example of a cut point under the canonical metric.
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arxiv.org
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