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...

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

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

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

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

geometry" was introduced to refer to the older methods that were, before Descartes, the only known ones. According to Felix Klein Synthetic geometry is...

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

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

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

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

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

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...

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

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

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...

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

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...

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

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

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

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...

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

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry...

time-series into 2D manifolds (kime-surfaces). According to Klein's definition, "a geometry is the study of the invariant properties of a spacetime, under...

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...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

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

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...

systematic effort to use transformations as the foundation of geometry was made by Felix Klein in the 19th century, under the name Erlangen programme. For...