Characterization of manifolds of constant curvature by spherical curves

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, the given manifold has constant sectional curvature. We also furnish two other characterizations in terms of (i) an inequality involving the mean curvature of a geodesic sphere and the curvature function of their curves and (ii) the vanishing of the total torsion of closed spherical curves in the case of three-dimensional manifolds. Finally, we also show that the same results are valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat

Heavy ion collisions at intermediate energies in a quark-gluon exchange framework

Heavy ion collisions at intermediate energies can be studied in the context of the Vlasov-Uehling-Uhlenbeck (VUU) model. One of the main features in this model is the nucleon-nucleon (NN) cross section in the collisional term. Quark interchange plays a role in the NN interaction and its effect can be observed in the cross section. We explore the possibility that quark interchange effects can appear in observables at energies lower than RHIC.Comment: To appear in the Proceedings of VIII Hadron Physics 200

Meson decay in the Fock-Tani Formalism

The Fock-Tani formalism is a first principle method to obtain effective interactions from microscopic Hamiltonians. Usually this formalism was applied to scattering, here we introduced it to calculate partial decay widths for mesons.Comment: Presented at HADRON05 XI. "International Conference on Hadron Spectroscopy" Rio de Janeiro, Brazil, August 21 to 26, 200

Meson decay in a corrected 30P3^P_0 model

Extensively applied to both light and heavy meson decay and standing as one of the most successful strong decay models is the $3^P_0$ model, in which $q\bar{q}$ pair production is the dominant mechanism. The pair production can be obtained from the non-relativistic limit of a microscopic interaction Hamiltonian involving Dirac quark fields. The evaluation of the decay amplitude can be performed by a diagrammatic technique for drawing quark lines. In this paper we use an alternative approach which consists in a mapping technique, the Fock-Tani formalism, in order to obtain an effective Hamiltonian starting from same microscopic interaction. An additional effect is manifest in this formalism associated to the extended nature of mesons: bound-state corrections. A corrected $3^P_0$ is obtained and applied, as an example, to $b_{1}\to\omega\pi$ and $a_{1}\to\rho\pi$ decays.Comment: 3 figures. To appear in Physical Review