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Functional Analysis and Its Applications, 1987
The classical Gauss map \(\gamma\) : \(X^ n\to G(N,n)\) associates to a point x of a nonsingular projective algebraic variety \(X^ n\subset {\mathbb{P}}^ N\) the point in the Grassmann variety G(N,n) of n-dimensional linear subspaces in \({\mathbb{P}}^ N\) corresponding to the embedded tangent space \(T_{X,x}\) to X at x.
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The classical Gauss map \(\gamma\) : \(X^ n\to G(N,n)\) associates to a point x of a nonsingular projective algebraic variety \(X^ n\subset {\mathbb{P}}^ N\) the point in the Grassmann variety G(N,n) of n-dimensional linear subspaces in \({\mathbb{P}}^ N\) corresponding to the embedded tangent space \(T_{X,x}\) to X at x.
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Every Meromorphic Function is the Gauss Map of a Conformal Minimal Surface
, 2016Let M be an open Riemann surface. We prove that every meromorphic function on M is the complex Gauss map of a conformal minimal immersion $$M\rightarrow \mathbb {R}^3$$M→R3 which may furthermore be chosen as the real part of a holomorphic null curve $$M ...
A. Alarcón +2 more
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Characteristic cycles and the microlocal geometry of the Gauss map, I
Annales Scientifiques de l'Ecole Normale Supérieure, 2016Continuing the study of the reductive Tannaka groups defined by holonomic D-modules on abelian varieties, we show that up to isogeny every Weyl group orbit of weights for their universal cover is realized by a conic Lagrangian cycle on the cotangent ...
Thomas R. Kramer
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1979
An oriented n-surface in ℝ n +l is more than just an n-surface S, it is an n-surface S together with a smooth unit normal vector field N on S. The function N:S → ℝ n +1 associated with the vector field N by N(p) = (p, N(p)), p ∈ S, actually maps S into the unit n-sphere S n ⊂ ℝ n +1 since ∥N(p)∥ = 1 for all p ∈ S.
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An oriented n-surface in ℝ n +l is more than just an n-surface S, it is an n-surface S together with a smooth unit normal vector field N on S. The function N:S → ℝ n +1 associated with the vector field N by N(p) = (p, N(p)), p ∈ S, actually maps S into the unit n-sphere S n ⊂ ℝ n +1 since ∥N(p)∥ = 1 for all p ∈ S.
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1996
The classical Gauss map is important in the minimal surface theory of 3-dimensional Euclidean space. For general submanifolds in Euclidean space we can define a generalized Gauss map. In many cases properties of submanifolds are characterized by their Gauss maps and closely link with the theory of harmonic maps.
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The classical Gauss map is important in the minimal surface theory of 3-dimensional Euclidean space. For general submanifolds in Euclidean space we can define a generalized Gauss map. In many cases properties of submanifolds are characterized by their Gauss maps and closely link with the theory of harmonic maps.
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Boundary crises and supertrack orbits in the Gauss map
The European Physical Journal Special Topics, 2022Juliano A. de Oliveira +4 more
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GM-CPSO: A New Viewpoint to Chaotic Particle Swarm Optimization via Gauss Map
Neural Processing Letters, 2020Hasan Koyuncu
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Continued fractions and the Gauss map
2005Summary: We discover properties of the Gauss map and its iterates using continued fractions. In particular, we find all fixed points and show that the graph of an iterate over \([0,1/2]\) is symmetric to the graph of the next higher iterate over \([1/2,1]\).
Bates, Bruce +2 more
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The Harmonicity of the Spherical Gauss Map
Bulletin of the London Mathematical Society, 1986Given an isometric immersion \(f: M^ m\to {\mathbb{R}}^ n\), its generalized Gauss map g in the sense of Chern and Osserman is the map \(g: M\to G_ m({\mathbb{R}}^ n)\), assigning to each point p in M the tangent space at p of M viewed as an m-dimensional plane in \({\mathbb{R}}^ n\). An easy yet vitally important theorem of \textit{E. A.
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Cheng–Yau Operator and Gauss Map of Rotational Hypersurfaces in 4-Space
Mediterranean Journal of Mathematics, 2019Erhan Güler, N. Turgay
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