Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a geodesic sphere or totally geodesic hypersurface in a Riemannian manifold of constant curvature. Using that geodesic spherical curves are normal curves, i.e., they are the image of an Euclidean spherical curve under the exponential map, we are able to characterize geodesic spherical curves in hyperbolic spaces and spheres through a non-homogeneous linear equation. Finally, we also show that curves on totally geodesic hypersurfaces, which play the role of hyperplanes in Riemannian geometry, should be characterized by a homogeneous linear equation. In short, our results give interesting and significant similarities between hyperbolic, spherical, and Euclidean geometries.Comment: 15 pages, 3 figures; comments are welcom

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

Anisotropic simplicial minisuperspace model

The computation of the simplicial minisuperspace wavefunction in the case of anisotropic universes with a scalar matter field predicts the existence of a large classical Lorentzian universe like our own at late timesComment: 19 pages, Latex, 6 figure

Self-Adaptive Role-Based Access Control for Business Processes

© 2017 IEEE. We present an approach for dynamically reconfiguring the role-based access control (RBAC) of information systems running business processes, to protect them against insider threats. The new approach uses business process execution traces and stochastic model checking to establish confidence intervals for key measurable attributes of user behaviour, and thus to identify and adaptively demote users who misuse their access permissions maliciously or accidentally. We implemented and evaluated the approach and its policy specification formalism for a real IT support business process, showing their ability to express and apply a broad range of self-adaptive RBAC policies