Results 131 to 140 of about 2,226,189 (161)
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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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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map
International Electronic Journal of Geometry, 2023Bang-Yen Chen +2 more
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On the Gauss map of submanifolds. I.
Let \(M\) be a submanifold isometrically immersed in \(N\), a hypersurface of the Euclidean space \(E^{n+1}\). The author studies the Gauss map of \(M\) and by determining the differential of the Gauss map, the relationships among the Ricci curvature, the second and the third fundamental forms of \(M\) are established.openaire +2 more sources
SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP
Journal of the Korean Mathematical Society, 2005Bang-Yen Chen, Young Ho Kim
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MERIDIAN SURFACES IN ?4WITH POINTWISE 1-TYPE GAUSS MAP
Bulletin of the Korean Mathematical Society, 2014Betul Bulca +2 more
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