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}}...

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc...

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...

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...

mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical...

Liouville surface, another generalization of a surface of revolution Spheroid Surface integral Translation surface (differential geometry) Middlemiss;...

{\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...

Spherical geometry is a form of elliptic geometry, which together with hyperbolic geometry makes up non-Euclidean geometry. The sphere is a smooth surface with...

mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent...

demonstrate how minimal surface theory lies at the crossroads of several mathematical disciplines, especially differential geometry, calculus of variations...

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...

In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in R 3 {\displaystyle \mathbb {R} ^{3}} that is invariant under...

manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For...

given (at least locally) as the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition...

Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative...

{OP}}.} The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus. Frequently this is...

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...

C. Burali-Forti, "Introduction to Differential Geometry, following the method of H. Grassmann" (English translation of book) E. Kummer, "General theory...

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...

solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic...

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel...

the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been reworked...

foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system...

In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the surface...

In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to...

In differential geometry, Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published...

manifolds. The theorem is foundational in differential topology and calculus on manifolds. Contact geometry studies 1-forms that maximally violates the...

who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first...