Caracterización de variedades riemannianas mediante curvaturas escalares totais de esferas xeodésicas

In order to study Riemannian manifolds, certain geometrical objects naturally associated to the structure of the manifold are usually considered. Curvature is, by far, the more broadly studied of those objects since the very beginning of Riemannian Geometry. Curvature largely in°uences the geometrical properties of the manifold and can even determine its topology. Nevertheless, the curvature of a manifold is often di±cult to handle and, as a consequence, certain simpli¯cations are used. In this work, we will focus on what are known as scalar curvature invariants and their role in determining the local geometry of a manifold.