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

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}}...

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

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

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

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...

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

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...

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

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

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...

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

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...

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

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...

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...

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...

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...

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

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

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

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

{\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...

In mathematics, differential forms on a Riemann surface are an important special case of the general theory of differential forms on smooth manifolds...

In the mathematical field of differential geometry a Liouville surface (named after Joseph Liouville) is a type of surface which in local coordinates may...

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

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

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

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...

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...