55,547 research outputs found
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 model
Extensively applied to both light and heavy meson decay and standing as one
of the most successful strong decay models is the model, in which
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 is obtained and applied, as an example, to
and decays.Comment: 3 figures. To appear in Physical Review
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