Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Download
Faster access than browser!
 

Conformal geometry and Möbius transformation

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Conformal geometry and Möbius transformation

Conformal geometry vs. Möbius transformation

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

Similarities between Conformal geometry and Möbius transformation

Conformal geometry and Möbius transformation have 23 things in common (in Unionpedia): Borel subgroup, Celestial sphere, Complex plane, Conformal geometry, Conformal map, Covering space, Erlangen program, Geometry, Group action, Holomorphic function, Inversive geometry, Isometry, Liouville's theorem (conformal mappings), Minkowski space, N-sphere, Null vector, Projective linear group, Quadratic form, Riemann sphere, Riemann surface, Riemannian manifold, Stereographic projection, Up to.

Borel subgroup

In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup.

Borel subgroup and Conformal geometry · Borel subgroup and Möbius transformation · See more »

Celestial sphere

In astronomy and navigation, the celestial sphere is an abstract sphere with an arbitrarily large radius concentric to Earth.

Celestial sphere and Conformal geometry · Celestial sphere and Möbius transformation · See more »

Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

Complex plane and Conformal geometry · Complex plane and Möbius transformation · See more »

Conformal geometry

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.

Conformal geometry and Conformal geometry · Conformal geometry and Möbius transformation · See more »

Conformal map

In mathematics, a conformal map is a function that preserves angles locally.

Conformal geometry and Conformal map · Conformal map and Möbius transformation · See more »

Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

Conformal geometry and Covering space · Covering space and Möbius transformation · See more »

Erlangen program

The Erlangen program is a method of characterizing geometries based on group theory and projective geometry.

Conformal geometry and Erlangen program · Erlangen program and Möbius transformation · See more »

Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Conformal geometry and Geometry · Geometry and Möbius transformation · See more »

Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

Conformal geometry and Group action · Group action and Möbius transformation · See more »

Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

Conformal geometry and Holomorphic function · Holomorphic function and Möbius transformation · See more »

Inversive geometry

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.

Conformal geometry and Inversive geometry · Inversive geometry and Möbius transformation · See more »

Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.

Conformal geometry and Isometry · Isometry and Möbius transformation · See more »

Liouville's theorem (conformal mappings)

In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, is a rigidity theorem about conformal mappings in Euclidean space.

Conformal geometry and Liouville's theorem (conformal mappings) · Liouville's theorem (conformal mappings) and Möbius transformation · See more »

Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

Conformal geometry and Minkowski space · Möbius transformation and Minkowski space · See more »

N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

Conformal geometry and N-sphere · Möbius transformation and N-sphere · See more »

Null vector

In mathematics, given a vector space X with an associated quadratic form q, written, a null vector or isotropic vector is a non-zero element x of X for which.

Conformal geometry and Null vector · Möbius transformation and Null vector · See more »

Projective linear group

In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V).

Conformal geometry and Projective linear group · Möbius transformation and Projective linear group · See more »

Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

Conformal geometry and Quadratic form · Möbius transformation and Quadratic form · See more »

Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

Conformal geometry and Riemann sphere · Möbius transformation and Riemann sphere · See more »

Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

Conformal geometry and Riemann surface · Möbius transformation and Riemann surface · See more »

Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

Conformal geometry and Riemannian manifold · Möbius transformation and Riemannian manifold · See more »

Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

Conformal geometry and Stereographic projection · Möbius transformation and Stereographic projection · See more »

Up to

In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.

Conformal geometry and Up to · Möbius transformation and Up to · See more »

The list above answers the following questions

Conformal geometry and Möbius transformation Comparison

Conformal geometry has 73 relations, while Möbius transformation has 158. As they have in common 23, the Jaccard index is 9.96% = 23 / (73 + 158).

References

This article shows the relationship between Conformal geometry and Möbius transformation. To access each article from which the information was extracted, please visit:

Hey! We are on Facebook now! »