Spline Interpolation on Other Riemannian Manifolds

In this chapter, our objective is to extend and validate the methodology introduced in previous chapters to encompass additional cases of symmetric Riemannian manifolds. Specifically, we focus on two such instances: the set of symmetric and positive-definite matrices (SPD), denoted as \(\mathcal {P}_{n}^{+}\) , and hyperbolic spaces \(\mathcal {H}_{n}\) characterized by constant negative curvature. These nonlinear spaces find wide-ranging applications where the demand for smooth interpolating splines is pronounced.