GEODESIC TUBES AND SPACES OF CONSTANT CURVATURE

This is a contribution to the general problem of how the properties of geodesic tubes on a Riemannian manifold ＄(M^{n}, g)＄ determine the geometry of the ambient space. Using Jacobi vector fields and Fermi coordinates, we characterize spaces of constant sectional curvature by means of the shape operator of small enough geodesic tubes.