Results 181 to 190 of about 288 (215)
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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Some of the next articles are maybe not open access.
On Umbilic Points on Newly Born Surfaces
Bulletin of the Brazilian Mathematical Society, 2017The authors show that newly born surfaces in 3-space have 4 and only 4 umbilic points. Umbilics are points on a surface where the curvature is the same in any direction. That is, locally, the surface is spherical. Here, a newly born surface is characterized as a surface created from a function with Morse singularity of index either 0 or 3.
Farid Tari, Hasegawa Masaru
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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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On the Moser normal form at a non-umbilic point
Mathematische Annalen, 1978 Any analytic real hypersurface \(M^{2n+1}\) in \(\mathbb{C}^{n+1}\), \(n\geq 1\)with non-degenerate Levi form at a point \(p\) has a normal form relative to certain holomorphic coordinate systems centered at \(p\) [\textit{S. S. Chern} and \textit{J. K. Moser}, Acta math. 133 (1974), 219-271 (1975; Zbl 0302.32015)].
S M Webster, Webster S M
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Umbilic point screening in random optical fields
Optics Letters, 2007Umbilic points--singular points of curvature characterized by a fractional topological charge q=+/-1/2--are the most numerous of all special points in the landscape of random optical fields (speckle patterns), outnumbering maxima, minima, saddle points, and optical vortices.
Isaac, Freund +2 more
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Lines of curvature and umbilical points for implicit surfaces
Computer Aided Geometric Design, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Che, Wu-Jun +2 more
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Umbilic points on Gaussian random surfaces
Journal of Physics A: Mathematical and General, 1977An umbilic point U on a surface Sigma is a place where the two principal curvatures of Sigma are equal. U is a singularity of Sigma in three different senses: (i) it is the source of elliptic (E) or hyperbolic (H) umbilic catastrophes in the envelope of normals ('focal surface') of Sigma ; (ii) it has index +or-1/2 depending on whether the principal ...
Berry, M. V., Hannay, J. H.
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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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