Curvaturas totais de esferas xeodésicas

In order to study Riemannian manifolds, certain geometrical objects naturally associated to the structure of the manifold (M; g) itself are broadly used. As an instance of such geometrical objects, we have the different fiber bundles with basis (M; g) (for example, the bundle of linear frames, the tangent bundle, the spheric tangent bundle, etc.), certain kinds of local transformations on the manifold (which allow us to determine its symmetries) or hypersurfaces which reflect certain properties of the ambient manifold. Among the latter, geodesic spheres of sufficiently small radius, which are the starting point of this work, are specially important.