• Thumbnail for Differential geometry of surfaces
    In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...
    128 KB (17,447 words) - 02:21, 18 August 2024
  • Thumbnail for Differential geometry
    and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during...
    46 KB (5,912 words) - 08:09, 21 August 2024
  • on which Geometry is Based"). It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian...
    13 KB (1,471 words) - 09:45, 15 August 2024
  • Thumbnail for Translation surface (differential geometry)
    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}}...
    9 KB (1,661 words) - 00:16, 28 January 2024
  • 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...
    8 KB (679 words) - 11:05, 12 February 2024
  • Thumbnail for Surface (topology)
    mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical...
    32 KB (4,170 words) - 23:57, 20 April 2024
  • Thumbnail for Saddle point
    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...
    9 KB (1,010 words) - 13:20, 17 August 2024
  • 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...
    3 KB (299 words) - 22:17, 23 October 2021
  • Thumbnail for Gaussian 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...
    19 KB (2,612 words) - 22:21, 7 August 2024
  • Thumbnail for Theorema Egregium
    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...
    6 KB (694 words) - 18:20, 16 July 2024
  • 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...
    11 KB (1,125 words) - 05:28, 24 May 2024
  • Thumbnail for Surface (mathematics)
    open subset of the Euclidean plane (see Surface (topology) and Surface (differential geometry)). This allows defining surfaces in spaces of dimension higher...
    22 KB (3,955 words) - 14:39, 13 August 2024
  • Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are...
    1 KB (136 words) - 19:04, 13 July 2024
  • Thumbnail for Principal curvature
    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...
    10 KB (1,290 words) - 06:48, 1 May 2024
  • Thumbnail for Minimal surface
    surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of...
    21 KB (2,718 words) - 08:16, 9 February 2024
  • 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...
    11 KB (1,739 words) - 00:25, 20 August 2024
  • intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas. Because of the blend of techniques...
    26 KB (3,677 words) - 14:31, 7 September 2023
  • 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...
    23 KB (3,326 words) - 14:19, 30 May 2024
  • 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...
    23 KB (3,546 words) - 16:26, 15 August 2023
  • Thumbnail for Developable surface
    In three dimensions all developable surfaces are ruled surfaces (but not vice versa). There are developable surfaces in four-dimensional space ⁠ R 4 {\displaystyle...
    6 KB (675 words) - 15:11, 17 April 2024
  • Thumbnail for Sum of angles of a triangle
    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...
    7 KB (815 words) - 04:12, 12 August 2024
  • Frederick. Principles of geometry. Vol. 2. CUP Archive, 1954. Carmo, Manfredo Perdigão do (1976). Differential geometry of curves and surfaces. Vol. 2. Englewood...
    100 KB (9,886 words) - 03:41, 24 August 2024
  • 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...
    3 KB (306 words) - 22:14, 9 July 2024
  • Thumbnail for Ruled surface
    1007/s00004-011-0087-z do Carmo, Manfredo P. (1976), Differential Geometry of Curves and Surfaces (1st ed.), Prentice-Hall, ISBN 978-0132125895 Barth,...
    18 KB (2,884 words) - 13:34, 29 July 2024
  • 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...
    35 KB (5,029 words) - 23:36, 30 May 2024
  • Thumbnail for Differential topology
    closely related field of differential geometry, which concerns the geometric properties of smooth manifolds, including notions of size, distance, and rigid...
    15 KB (1,837 words) - 18:20, 27 July 2023
  • 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...
    10 KB (1,454 words) - 20:34, 18 January 2024
  • 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)...
    4 KB (689 words) - 17:07, 14 April 2022
  • Thumbnail for Geometric analysis
    Geometric analysis (category Differential geometry)
    from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and...
    4 KB (473 words) - 19:56, 28 June 2023
  • Thumbnail for Symplectic geometry
    Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...
    11 KB (1,313 words) - 21:08, 10 June 2024