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
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
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
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
Pseudosphere (redirect from Pseudospherical surface)
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
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
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
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
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
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
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
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
{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
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
Genus (mathematics) (redirect from Genus (geometry))
{\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
Bernstein's problem (redirect from Bernstein problem in differential geometry)
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
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
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