Paneitz operator
In the mathematical field of differential geometry, the Paneitz operator is a fourth-order differential operator defined on a Riemannian manifold of dimension n. It is named after , who discovered it
Conformally flat manifold
A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation. In practice, the metric of the manifold has to be co
Lie sphere geometry
Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. It was introduced by Sophus Lie in the nineteenth century. The main
Conformal group
In mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that pres
Fundamental polygon
In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only the topology of the surface through its fundamental group but also d
Polyakov formula
In differential geometry and mathematical physics (especially string theory), the Polyakov formula expresses the conformal variation of the zeta functional determinant of a Riemannian manifold. The co
Problem of Apollonius
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 BC – c. 190 BC) posed and solved th
Tractor bundle
In conformal geometry, the tractor bundle is a particular vector bundle constructed on a conformal manifold whose fibres form an effective representation of the conformal group (see associated bundle)
Poincaré metric
In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a v
Conformal connection
In conformal differential geometry, a conformal connection is a Cartan connection on an n-dimensional manifold M arising as a deformation of the Klein geometry given by the celestial n-sphere, viewed
Conformal geometry
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of
Band model
In geometry, the band model is a conformal model of the hyperbolic plane. The band model employs a portion of the Euclidean plane between two parallel lines. Distance is preserved along one line throu
Conformal gravity
Conformal gravity refers to gravity theories that are invariant under conformal transformations in the Riemannian geometry sense; more accurately, they are invariant under Weyl transformations where i
Lorentz surface
In mathematics, a Lorentz surface is a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics. It is the analogue of a Riemann surface in indefinite signatur
Conformal geometric algebra
Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space Rp,q to null vectors in Rp+1,q+1. This allows operat
Möbius transformation
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 satisf
GJMS operator
In the mathematical field of differential geometry, the GJMS operators are a family of differential operators, that are defined on a Riemannian manifold. In an appropriate sense, they depend only on t
Poincaré half-plane model
In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H , together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic
Ambient construction
In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham for which a conformal manifold of dimension n is realized (ambiently) as the boundary of
Indra's Pearls (book)
Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002 and 2015. The book explores