Results 1 to 10 of about 264 (211)
A metric property of umbilic points [PDF]
Anais da Academia Brasileira de Ciências, 2003 In the space of cubic forms of surfaces, regarded as a G-space and endowed with a natural invariant metric, the ratio of umbilic points with a negative index to those with a positive index is evaluated in terms of the asymmetry of the metric, defined ...
Ronaldo Garcia, Jorge Sotomayor
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On the patterns of principal curvature lines around a curve of umbilic points [PDF]
Anais da Academia Brasileira de Ciências, 2005 In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.Neste trabalho estuda-se o comportamento das linhas de curvatura principal próximas a uma curva de pontos umbílicos, numa superfície ...
Ronaldo Garcia, Jorge Sotomayor
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On isolated umbilic points [PDF]
Communications in Analysis and Geometry, 2020 Counter-examples to the famous conjecture of Caratheodory, as well as the bound on umbilic index proposed by Hamburger, are constructed with respect to Riemannian metrics that are arbitrarily close to the flat metric on Euclidean 3-space. In particular, Riemannian metrics with a smooth strictly convex 2-sphere containing a single umbilic point are ...
Guilfoyle Brendan
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On the multiplicity of umbilic points
Pacific Journal of Mathematics, 2022 We introduce an invariant of umbilic points on surfaces in the Euclidean or Minkowski 3-space that counts the maximum number of stable umbilic points they can split up under deformations of the surfaces. We call that number the multiplicity of the umbilic point and establish its properties.
Marco Antonio Do Couto Fernandes +1 more
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Bifurcations of Umbilic Points and Related Principal Cycles [PDF]
Journal of Dynamics and Differential Equations, 2004 The simplest patterns of qualitative changes on the configurations of lines of principal curvature} around umbilic points on surfaces whose immersions into $\mathbb R^3$ depend smoothly on a real parameter (codimension one umbilic bifurcations) are described in this paper. Global effects, due to umbilic bifurcations, on these configurations such as the
R Garcia +2 more
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A note on umbilic points at infinity
Beitrage Zur Algebra Und GeometrieAbstract In this note a definition of umbilic point at infinity is proposed, at least for surfaces that are homogeneous polynomial graphs over a plane in Euclidean 3-space. This is a stronger definition than that of Toponogov in his study of complete convex surfaces, and allows one to distinguish between different umbilic points at infinity ...
Brendan Guilfoyle
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Codimension two umbilic points on surfaces immersed in $R^3$
Discrete and Continuous Dynamical Systems, 2007 In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.
R Garcia, Jorge Sotomayor
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Characterizations of Umbilic Points of Isometric Immersions in Riemannian and Lorentzian Manifolds
Taiwanese Journal of Mathematics, 2016 Several characterizations of umbilic points of submanifolds in arbitrary Riemannian and Lorentzian manifolds are given. As a consequence, we obtain new characterizations of spheres in the Euclidean space and of hyperbolic spaces in the Lorentz-Minkowski space. We also prove the Lorentzian version of a classical result by Cartan.
Magdalena Caballero Campos
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Manipulating self-focusing beams induced by high-dimensional parabolic umbilic beams
Results in Physics, 2023 The excellent property that the intensity of autofocusing beams in the focal plane increases exponentially, makes them especially beneficial for biomedical treatment.
Zhuo Sun +4 more
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Bifurcation of solutions through a contact manifold in bidisperse models
Frontiers in Applied Mathematics and Statistics, 2023 This research focuses on a hyperbolic system that describes bidisperse suspensions, consisting of two types of small particles dispersed in a viscous fluid.
Stefan Berres, Pablo Castañeda
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