tensor of conformal curvature

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• 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 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 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

• Weyl tensor — In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal… …   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

• 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

• Cotton tensor — In differential geometry, the Cotton tensor on a (pseudo) Riemannian manifold of dimension n is a third order tensor concomitant of the metric, like the Weyl tensor. The concept is named after Émile Cotton. Just as the vanishing of the Weyl… …   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

• Kretschmann scalar — In the theory of Lorentzian manifolds, particularly in the context of applications to general relativity, the Kretschmann scalar is a quadratic scalar invariant. It was introduced by Erich Kretschmann. DefinitionThe Kretschmann invariant is: K =… …   Wikipedia

• Spacetime symmetries — refers to aspects of spacetime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important, for example, in simplifying solutions to many problems. Spacetime symmetries are used to simplify problems and …   Wikipedia