pseudo-conformally
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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. More formally, let (M, g) be a pseudo Riemannian manifold. Then (M, g) is conformally flat if for… … 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
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
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
Ambient construction — In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham [Fefferman, C. and Graham, R. Conformal invariants , in Élie Cartan et les Mathématiques d Aujourdui , Asterisque (1985), 95 116.] for… … 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
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
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
