In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous...

hyperbolic geometry, elliptic geometry, and Euclidean geometry. The field of non-Euclidean geometry rests largely on the footing provided by Cayley–Klein metrics...

experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest was mainly geometry. Klein received his doctorate, supervised...

interesting cosmological models. The Kaluza–Klein theory has a particularly elegant presentation in terms of geometry. In a certain sense, it looks just like...

Euclidean geometry, they described their geometry under many different names; Felix Klein finally gave the subject the name hyperbolic geometry to include...

According to Felix Klein Synthetic geometry is that which studies figures as such, without recourse to formulae, whereas analytic geometry consistently makes...

Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry. A conformal manifold is a Riemannian manifold (or pseudo-Riemannian...

geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Noncommutative...

geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry...

is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix Klein in 1872 as Vergleichende Betrachtungen...

geometry extends the notion of a Klein geometry by attaching to each point of a manifold a copy of a Klein geometry, and to regard this copy as tangent...

topology Klein geometry Klein configuration, in geometry Klein cubic (disambiguation) Klein graphs, in graph theory Klein model, or Beltrami–Klein model, a...

non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the...

Projective geometry, like affine and Euclidean geometry, can also be developed from the Erlangen program of Felix Klein; projective geometry is characterized...

cohomology elliptic complex Hodge theory pseudodifferential operator Klein geometry, Erlangen programme symmetric space space form Maurer–Cartan form Examples...

elliptic geometry when he wrote "On the definition of distance".: 82  This venture into abstraction in geometry was followed by Felix Klein and Bernhard...

Möbius wrote on affine geometry in his Der barycentrische Calcul (chapter 3). After Felix Klein's Erlangen program, affine geometry was recognized as a generalization...

identifying tangent spaces with the tangent space of a certain model Klein geometry Ehresmann connection, gives a manner for differentiating sections of...

have a point of contact with a certain model Klein geometry at each point. In extrinsic differential geometry, the soldering is simply expressed by the tangency...

was in the new geometries of Bolyai and Lobachevsky, Riemann, Clifford and Klein, and Sophus Lie that Klein's idea to 'define a geometry via its symmetry...

notably Clifford–Klein forms Γ\G/H, where Γ is a discrete subgroup (of G) acting properly discontinuously. For example, in the line geometry case, we can...

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical...

name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic geometry similar to Euclidean geometry but without the parallel postulate...

surfaces are Klein geometries in the sense of Felix Klein's Erlangen programme. More generally, an n-dimensional affine space is a Klein geometry for the affine...

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

Subsequently, Felix Klein studied projective geometry (along with other types of geometry) from the viewpoint that the geometry on a space is encoded...

In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines...

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...

In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts...

these geometries and more: his connection concept allowed for the presence of curvature which would otherwise be absent in a classical Klein geometry. (See...