In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...
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and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during...
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on which Geometry is Based"). It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian...
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In differential geometry a translation surface is a surface that is generated by translations: For two space curves c 1 , c 2 {\displaystyle c_{1},c_{2}}...
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This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...
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mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical...
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Saddle point (redirect from Saddle surface)
hyperbolic paraboloid shape. Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian...
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field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal...
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Gaussian curvature (redirect from Gaussian radius of curvature)
In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal...
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Theorema Egregium (category Differential geometry of surfaces)
Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says that...
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open subset of the Euclidean plane (see Surface (topology) and Surface (differential geometry)). This allows defining surfaces in spaces of dimension higher...
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Pseudosphere (redirect from Pseudospherical surfaces)
In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. A pseudosphere of radius R is a surface in R 3 {\displaystyle \mathbb...
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Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are...
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Principal curvature (redirect from Principal directions (geometry))
In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed...
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surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of...
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Mean curvature (category Differential geometry of surfaces)
H {\displaystyle H} of a surface S {\displaystyle S} is an extrinsic measure of curvature that comes from differential geometry and that locally describes...
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intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas. Because of the blend of techniques...
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Differentiable curve (redirect from Differential geometry of curves)
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential...
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Darboux frame (category Differential geometry of surfaces)
In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame...
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In three dimensions all developable surfaces are ruled surfaces (but not vice versa). There are developable surfaces in four-dimensional space R 4 {\displaystyle...
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hyperbolic case. In the differential geometry of surfaces, the question of a triangle's angular defect is understood as a special case of the Gauss-Bonnet theorem...
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Frederick. Principles of geometry. Vol. 2. CUP Archive, 1954. Carmo, Manfredo Perdigão do (1976). Differential geometry of curves and surfaces. Vol. 2. Englewood...
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Asymptotic curve (category Differential geometry of surfaces)
In the differential geometry of surfaces, an asymptotic curve is a curve always tangent to an asymptotic direction of the surface (where they exist). It...
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Scalar curvature (category Riemannian geometry)
characterized by the volume of infinitesimally small geodesic balls. In the context of the differential geometry of surfaces, the scalar curvature is twice...
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1007/s00004-011-0087-z do Carmo, Manfredo P. (1976), Differential Geometry of Curves and Surfaces (1st ed.), Prentice-Hall, ISBN 978-0132125895 Barth,...
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closely related field of differential geometry, which concerns the geometric properties of smooth manifolds, including notions of size, distance, and rigid...
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Second fundamental form (category Differential geometry of surfaces)
In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional...
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Simons' formula (category Differential geometry of surfaces)
In the mathematical field of differential geometry, the Simons formula (also known as the Simons identity, and in some variants as the Simons inequality)...
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Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...
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Gauss–Codazzi equations (category Differential geometry of surfaces)
the above formulas also hold for immersions. In classical differential geometry of surfaces, the Codazzi–Mainardi equations are expressed via the second...
14 KB (2,482 words) - 02:29, 22 May 2024