conformal curvature

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• Conformal geometry — In mathematics, conformal geometry is the study of the set of angle preserving (conformal) transformations on a space. In two real dimensions, conformal geometry is precisely the geometry of Riemann surfaces. In more than two dimensions,… …   Wikipedia

• Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… …   Wikipedia

• Conformal Cyclic Cosmology — The Conformal Cyclic Cosmology (CCC) is a cosmological model in the framework of general relativity, advanced by the theoretical physicist Sir Roger Penrose.[1][2] In CCC, the universe iterates through infinite cycles, with the future timelike… …   Wikipedia

• Conformal map — For other uses, see Conformal (disambiguation). A rectangular grid (top) and its image under a conformal map f (bottom). It is seen that f maps pairs of lines intersecting at 90° to pairs of curves still intersecting at 90°. In mathematics, a… …   Wikipedia

• Conformal vector field — A conformal vector field (often conformal Killing vector field and occasionally conformal or conformal collineation) of a Riemannian manifold (M,g) is a vector field X that satisfies: for some smooth real valued function φ on M, where denotes the …   Wikipedia

• Curvature collineation — A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that, where Rabcd are the components of the Riemann tensor. The set of all smooth curvature collineations forms a Lie algebra under …   Wikipedia

• Ricci curvature — In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci Curbastro, provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n… …   Wikipedia

• Scalar curvature — In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the… …   Wikipedia

• Prescribed scalar curvature problem — In Riemannian geometry, a branch of mathematics, the prescribed scalar curvature problem is as follows: given a closed, smooth manifold M and a smooth, real valued function f on M , construct a Riemannian metric on M whose scalar curvature equals …   Wikipedia

• Weyl curvature hypothesis — The Weyl curvature hypothesis, which arises in the application of Albert Einstein s general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979… …   Wikipedia

• Ricci decomposition — In semi Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a pseudo Riemannian manifold into pieces with useful individual algebraic properties. This decomposition is of fundamental importance in… …   Wikipedia