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...

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...

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...

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...

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

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

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

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

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...

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

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...

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...

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...

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....

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...

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

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...

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

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...

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...

In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical...

In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It...

Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...