Riemannian cubics close to geodesics at the boundaries

Abstract

<p style='text-indent:20px;'>In this paper we investigate the existence and uniqueness of Riemannian cubics under boundary conditions on position and velocity. We restrict the study to cubics close to geodesics at the boundaries. In other words, we consider the boundary data in a neighborhood of geodesic boundary data. We define a map that generalizes the Riemannian exponential, the biexponential. This map is used to establish the correspondence between initial and boundary data. We also emphasize the relation between biconjugate points and bi-Jacobi fields along cubics by means of the biexponential map.</p>