Results 11 to 20 of about 384 (243)
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.
Garcia, Ronaldo, Sotomayor, Jorge
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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 here.
Garcia, Ronaldo, Sotomayor, Jorge
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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.
do Couto Fernandes, Marco Antônio +1 more
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A note on umbilic points at infinity
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2023 Abstract 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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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
Gutiérrez, Carlos +2 more
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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.
Garcia, Ronaldo, Sotomayor, Jorge
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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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Perestroikas of vertex sets at umbilic points [PDF]
Functional Analysis and Other Mathematics, 2008 Mark all vertices on a curve evolving under a family of curves obtained by intersecting a smooth surface M with the 1-parameter family of planes parallel to the tangent plane to M at a point p. Those vertices trace out a set, called the vertex set of M through p. We take p to be an isolated umbilic point on M and describe the perestroikas of the vertex
Capitanio, Gianmarco, Diatta, André
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Umbilic Lines in Orientational Order [PDF]
Physical Review X, 2016 Three-dimensional orientational order in systems whose ground states possess nonzero gradients typically exhibits linelike structures or defects: λ lines in cholesterics or Skyrmion tubes in ferromagnets, for example. Here, we show that such lines can be
Thomas Machon, Gareth P. Alexander
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An index bound for smooth umbilic points
, 2012 10 pages 3 figures AMS-LateX. A series of expository video clips explaining the methods and results of this paper can be found at the following links: https://www.youtube.com/watch?v=ybop3dETUjc and https://youtu.be ...
Guilfoyle, Brendan, Klingenberg, Wilhelm
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