Results 1 to 10 of about 398 (251)
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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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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Image formation near hyperbolic umbilic in strong gravitational lensing
The Open Journal of AstrophysicsHyperbolic umbilic (HU) is a point singularity of the gravitational lens equation, giving rise to a ring-shaped image formation made of four highly magnified images, off-centred from the lens centre.
Ashish Kumar Meena, Jasjeet Singh Bagla
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Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms [PDF]
Journal of Sciences, Islamic Republic of Iran, 2009 We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity.
S.M.B. Kashani
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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 ...
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Umbilic and Tangential Singularities on Configurations of Principal Curvature Lines
Anais da Academia Brasileira de Ciências, 2002 In this paper is studied the relationship between quadratic tangencies of principal lines with the boundary of a surface and the Darbouxian umbilics of a smooth boundaryless surface which approximates it through the process of thickening and smoothing ...
RONALDO GARCIA, JORGE SOTOMAYOR
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Shape operator of an $ (n-1) $-dimensional distribution on an $ n $-dimensional manifold and their classification [PDF]
ریاضی و جامعهThis paper aims to study of shape operator of an $ (n-1) $-dimensional distribution on an $ n $-dimensional smooth manifold. In this study firstly we state formulae for the shape operator and its symmetric and anti-symmetric components and in ...
Mehran Aminian, Mehran Namjoo
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On parabolic and umbilic points of immersed hypersurfaces [PDF]
Transactions of the American Mathematical Society, 1967 Introduction. This paper is a natural sequel to Geometry of immersions. I and II ([1] and [2]). The object is to apply the general geometric singularity theory developed in [1] and [2] to two specific geometric singularities of an immersed n manifold in R'+ll.
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Umbilic Points on the Finite and Infinite Parts of Certain Algebraic Surfaces
Mathematical Proceedings of the Royal Irish Academy, 2023 Abstract: The global qualitative behaviour of fields of principal directions for the graph of a real-valued polynomial function f on the plane is studied. We determine and analyse the projective extension of these fields and show that they are defined by an analytic quadratic form on the whole unit 2-sphere.
Guilfoyle, Brendan +1 more
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SLICE: SPT-CL J0546-5345—A Prominent Strong-lensing Cluster at z = 1.07
The Astrophysical Journal LettersMassive galaxy clusters act as prominent strong lenses. Due to a combination of observational biases, cluster evolution, and lensing efficiency, most of the known cluster lenses lie typically at z _l ∼ 0.2–0.7, with only a few prominent examples at ...
Joseph F. V. Allingham +17 more
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