Quadratic interpolation on spheres (Q1610217)

The author considers Riemannian quadratics which are \(C^1\) curves on Riemannian manifolds, obtained by performing the quadratic recursive deCastlejeau algorithm in a Riemannian setting. For interpolation problems in Riemannian manifolds these quadratics are of interest. Thus in this paper some interpolation properties of Riemannian quadratics are analysed when the ambient manifold is a sphere or a projective space provided with the usual Riemannian metric. After explaining the fundamental notions and connections, several examples are discussed.