Spline Interpolation on Stiefel and Grassmann Manifolds

In various real-world applications, the Stiefel and Grassmann manifolds are commonly employed for representation within Riemannian manifolds [1–3]. However, a persistent challenge in many of these applications stems from the intricate geometric structures inherent in these manifolds [4]. As real-world applications increasingly involve non-vector data, numerous algorithms for manifold embedding and manifold learning have been introduced to address these challenges. Recent efforts in this direction have focused on the development of essential geometric and statistical tools, including the Riemannian exponential map and its inverse, means, distributions, and geodesics [5–7].