Results 11 to 20 of about 398 (251)
A note on umbilic points at infinity
Beitrage Zur Algebra Und Geometrie, 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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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 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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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
Jorge Sotomayor +2 more
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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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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.
Jorge Sotomayor, Ronaldo Garcia
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Degenerate Umbilic Points of Analytic Surfaces
Umbilics are points of a surface embedded in three space where normal curvatures are independent of direction. The (in)famous Carathéodory Conjecture states that a compact simply connected embedded surface has at least two umbilic points. A counterexample to this conjecture would be a surface whose principal foliation has index two at a single umbilic.
Guckenheimaer, John
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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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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, Rafael M Rubio
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A study of horizontally weakly conformal maps and their distributions [PDF]
ریاضی و جامعه, 2023 The aim of this paper is to consider horizontally weakly conformal maps which have been studied in [P. Baird and J. C. Wood, Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs.
Mehran Aminian
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