Examinando por Materia "Geometry, riemannian"
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Ítem Funciones de Morse minimales en el espacio dodecaédrico de Poincaré, vía la Ecuación del Calor(Universidad EAFIT, 2014) Bernal Vera, Jhon Willington; Cadavid Moreno, Carlos AlbertoLet (M,g) be a compact, connected, without boundary riemannian manifold that is homogeneous, i.e. each pair of points p, q 2M have isometric neighborhoods -- This thesis is a another step towards an understanding of the extent to which it is true that for each “generic” initial condition f0, the solution to @f/@t = gf, f (·, 0) = f0 is such that for sufficiently large t, f (·, 0) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M -- In this thesis we show that for the Poincaré dodecahedral space this seems to hold if one allows a generic small perturbation of the metric -- Concretely, we consider an approximation of the spherical Poincaré dodecahedral space by a suitably weighted graph, calculate the eigenvalues and eigenvectors of its laplacian oparator, and study the critical point structure of eigenvectors of some of the first nonzero eigenvalues, and observe that they have the least possible number of critical pointsÍtem Manifold Learning with Orthogonal Geodesic Grids(2014) Ruíz, Óscar E.; Cadavid, Carlos; Ebratt, Roberto; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn Reverse Engineering, it is capital to find a parametric trimmed surface which approximates a triangular mesh (2-manifold with border) M in R3 -- This article proposes and implements a quasi isometry f: M -> R2 which allows a parameterization of M -- We consider quasi - developable 2- manifolds M in R3 -- f(p) = (u,w) with (u,w) being the coordinates of p in M under a grid of geodesic curves Ci(u) and Cj(w) on M -- We seek that the geodesic curves Ci(u) and Cj(w) be orthogonal to each other on M -- This means, that the Ci(u) should not cross each other, and each Ci(u) should intersect each Cj(w) in perpendicular mannerÍtem A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences(Springer Berlin Heidelberg, 2013) Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román; Universidad EAFIT. Departamento de Ciencias; Análisis Funcional y AplicacionesFor the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold. Loading... Geometric Science of InformationGeometric Science of Information Look Inside Chapter Metrics Downloads1K Provided by Bookmetrix Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedInÍtem A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences(Springer Berlin Heidelberg, 2013) Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román; Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones; Gabriel Loaiza (gloaiza@eafit.edu.co); Héctor R. Quiceno (hquiceno@eafit.edu.co); Análisis Funcional y AplicacionesFor the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built -- In this paper, the geometry induced on this manifold is characterized by q-divergence functionals -- This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections -- Moreover, the classical Amari´s α-connections appears as special case of the q−connections (q) -- The main result is the expected one, namely the zero curvature of the manifoldÍtem Sobre estructuras geométricas para modelos q-Exponenciales(Universidad EAFIT, 2014) Restrepo Zuleta, Marinela Andrea; Carvajal Fernández, Leonardo Fabio; Loaiza Ossa, Gabriel Ignacio