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Spherical hypersurfaces associated with the spherical Gauss map and Gauss map
Publicationes Mathematicae Debrecen, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jung, Sun Mi +2 more
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Exponentially Harmonic Maps, Gauss Maps and Gauss Sections
Mediterranean Journal of Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Generalized Gauss map and the geometry of strings
Annals of Physics, 1991The tangent planes to a Euclidean string world sheet conformally immersed in \({\mathbb{R}}^ n\) define a map from the Riemann surface defined by the world sheet into the Grassmannian \(G_{2,n}\) (which may be realized as a quadric \(Q_{n-2}\) in \({\mathbb{C}}P^{n-1})\).
Viswanathan, K. S. +2 more
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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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Applied Mathematics and Computation, 2007
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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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On the Structure of Submanifolds with Degenerate Gauss Maps
Geometriae Dedicata, 2001The authors study \(n\)-dimensional submanifolds \(X\) of the projective space \(P^N(\mathbb{C})\) from the point of view of degeneration of their Gauss mapping \(\gamma:X\to G(n,N)\), \(\gamma(x)\) stands for the tangent space to \(X\) at \(x\). Three basic types of submanifolds: cones, tangentially degenerate hypersurfaces and torsal submanifolds are
Akivis, Maks A., Goldberg, Vladislav V.
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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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