• 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...
    129 KB (17,641 words) - 15:58, 25 May 2025
  • 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) - 17:16, 17 March 2025
  • Thumbnail for Differential geometry
    Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...
    46 KB (5,964 words) - 21:55, 19 May 2025
  • 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 (4,171 words) - 04:39, 1 March 2025
  • 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...
    10 KB (1,106 words) - 11:43, 17 May 2025
  • mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent...
    27 KB (4,595 words) - 00:13, 7 May 2024
  • Thumbnail for Surface of revolution
    Liouville surface, another generalization of a surface of revolution Spheroid Surface integral Translation surface (differential geometry) Middlemiss;...
    11 KB (2,054 words) - 18:14, 15 January 2025
  • 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 Gaussian...
    6 KB (685 words) - 02:20, 12 April 2025
  • Thumbnail for Triply periodic minimal surface
    In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in R 3 {\displaystyle \mathbb {R} ^{3}} that is invariant under...
    10 KB (1,078 words) - 01:22, 27 December 2024
  • Thumbnail for Minimal surface
    demonstrate how minimal surface theory lies at the crossroads of several mathematical disciplines, especially differential geometry, calculus of variations...
    23 KB (2,993 words) - 10:56, 21 May 2025
  • methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc...
    102 KB (10,101 words) - 16:23, 8 May 2025
  • Thumbnail for Tangent
    Tangent (redirect from Tangent (geometry))
    vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves...
    26 KB (4,113 words) - 11:19, 25 May 2025
  • Thumbnail for Sphere
    Sphere (redirect from Sphere (geometry))
    A sphere (from Greek σφαῖρα, sphaîra) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at...
    41 KB (5,342 words) - 15:01, 12 May 2025
  • Gauss map (category Differential geometry of surfaces)
    In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to its normal direction, a unit vector that is...
    6 KB (817 words) - 16:20, 1 April 2025
  • Dupin indicatrix (category Differential geometry of surfaces)
    In differential geometry, the Dupin indicatrix is a method for characterising the local shape of a surface. Draw a plane parallel to the tangent plane...
    4 KB (373 words) - 10:04, 28 September 2024
  • Thumbnail for Spherical geometry
    Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of higher...
    15 KB (1,955 words) - 21:52, 19 April 2025
  • Thumbnail for Position (geometry)
    {OP}}.} The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus. Frequently this is...
    9 KB (1,215 words) - 04:50, 27 February 2025
  • Thumbnail for Riemann's minimal surface
    In differential geometry, Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published...
    2 KB (224 words) - 17:20, 28 January 2023
  • Thumbnail for Genus (mathematics)
    {\displaystyle s} is the number of singularities when properly counted. In differential geometry, a genus of an oriented manifold M {\displaystyle M} may be defined...
    10 KB (1,412 words) - 15:03, 2 May 2025
  • the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been reworked...
    70 KB (10,206 words) - 12:10, 30 April 2025
  • In differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function...
    6 KB (689 words) - 00:34, 5 April 2025
  • solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic...
    13 KB (914 words) - 10:26, 25 December 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 Frobenius theorem (differential topology)
    manifolds. The theorem is foundational in differential topology and calculus on manifolds. Contact geometry studies 1-forms that maximally violates the...
    28 KB (4,231 words) - 12:44, 26 May 2025
  • In mathematics, differential forms on a Riemann surface are an important special case of the general theory of differential forms on smooth manifolds...
    78 KB (11,073 words) - 22:20, 25 March 2024
  • In the mathematical field of differential geometry a Liouville surface (named after Joseph Liouville) is a type of surface which in local coordinates may...
    4 KB (523 words) - 04:13, 14 May 2025
  • foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system...
    40 KB (5,612 words) - 22:13, 23 December 2024
  • manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For...
    67 KB (10,058 words) - 03:02, 23 March 2025
  • Plane (mathematics) (category Surfaces)
    preserved. Differential geometry views a plane as a 2-dimensional real manifold, a topological plane which is provided with a differential structure....
    7 KB (1,672 words) - 13:03, 27 April 2025
  • Thumbnail for Contact geometry
    given (at least locally) as the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition...
    20 KB (2,527 words) - 20:50, 23 May 2025