Results 21 to 30 of about 2,113,538 (360)
Spheres and Tori as Elliptic Linear Weingarten Surfaces
Mathematics, 2022 The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric.
Dong-Soo Kim, Young Ho Kim, Jinhua Qian
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Canal surfaces with generalized 1-type Gauss map
, 2021 This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is ...
J. Qian, Mengfei Su, Young Ho Kim
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On Separable Higher Gauss Maps [PDF]
Michigan Mathematical Journal, 2019 We study the $m$-th Gauss map in the sense of F.~L.~Zak of a projective variety $X \subset \mathbb{P}^N$ over an algebraically closed field in any characteristic. For all integer $m$ with $n:=\dim(X) \leq m < N$, we show that the contact locus on $X$ of a general tangent $m$-plane is a linear variety if the $m$-th Gauss map is separable.
Furukawa, Katsuhisa, Ito, Atsushi
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Spherical Ruled Surfaces in S3 Characterized by the Spherical Gauss Map
Mathematics, 2020 The Laplace operator on a Riemannian manifold plays an important role with eigenvalue problems and the spectral theory. Extending such an eigenvalue problem of smooth maps including the Gauss map, the notion of finite-type was introduced.
Young Ho Kim, Sun Mi Jung
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SINGULARITIES OF HYPERBOLIC GAUSS MAPS [PDF]
Proceedings of the London Mathematical Society, 2003 In this paper we adopt the hyperboloid in Minkowski space as the model of hyperbolic space. We define the hyperbolic Gauss map and the hyperbolic Gauss indicatrix of a hypersurface in hyperbolic space. The hyperbolic Gauss map has been introduced by Ch. Epstein [J. Reine Angew. Math.
Izumiya, S., Pei, D-H, Sano, T.
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Mathematics in Engineering, 2023 We consider elastic thin shells without through-the-thickness shear and depict them as Gauss graphs of parametric surfaces. (We use the term shells to include plates and thin films therein.) We consider an energy depending on the first derivative of the ...
Paolo Maria Mariano, Domenico Mucci
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Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps
Mathematics, 2020 In the present work, the notion of generalized Cheng–Yau 1-type Gauss map is proposed, which is similar to the idea of generalized 1-type Gauss maps. Based on this concept, the surfaces of revolution and the canal surfaces in the Euclidean three-space ...
Jinhua Qian +3 more
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Conformal Gauss Map Geometry and Application to Willmore Surfaces in Model Spaces [PDF]
Potential Analysis, 2019 In this paper we make a detailed and self-contained study of the conformal Gauss map. Then, starting from the seminal work of Bryant (J. Differential Geom.
Nicolas Marque
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Journal of Physics: Conference Series, 2020 Chaos based cryptography has becoming an interesting topic lately, as it utilizes chaotic systems properties for secure key concealment. Many chaotic functions are discovered, constructed, and used time over time for this purpose, which will be our main ...
M. Suryadi +2 more
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Hypersurfaces with Generalized 1-Type Gauss Maps
Mathematics, 2018 In this paper, we study submanifolds in a Euclidean space with a generalized 1-type Gauss map. The Gauss map, G, of a submanifold in the n-dimensional Euclidean space, En, is said to be of generalized 1-type if, for the Laplace operator, Δ, on the ...
Dae Won Yoon +3 more
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