curvature of tensor

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• Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …   Wikipedia

• Curvature invariant (general relativity) — Curvature invariants in general relativity are a set of scalars called curvature invariants that arise in general relativity. They are formed from the Riemann, Weyl and Ricci tensors which represent curvature and possibly operations on them such… …   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

• Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia

• Curvature form — In differential geometry, the curvature form describes curvature of a connection on a principal bundle. It can be considered as an alternative to or generalization of curvature tensor in Riemannian geometry. Contents 1 Definition 1.1 Curvature… …   Wikipedia

• Curvature invariant — In Riemannian geometry and pseudo Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the Riemann tensor, the Weyl tensor, the Ricci tensor and tensors… …   Wikipedia

• Tensor field — In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of… …   Wikipedia

• Tensor contraction — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… …   Wikipedia

• Curvature tensor — In differential geometry, the term curvature tensor may refer to: the Riemann curvature tensor of a Riemannian manifold see also Curvature of Riemannian manifolds; the curvature of an affine connection or covariant derivative (on tensors); the… …   Wikipedia

• Tensor-Diagramm-Notation — Die penrosesche graphische Notation – auch als penrosesche diagrammatische Notation, Tensor Diagramm Notation oder auch einfach Penrose Notation bezeichnet – ist eine von Roger Penrose vorgeschlagene Notation in der Physik und Mathematik, um eine …   Deutsch Wikipedia

• Tensor de curvatura — En geometría diferencial, el tensor de curvatura de Riemann , o simplemente tensor de curvatura o tensor de Riemann, supone una generalización del concepto de curvatura de Gauss, definido para superficies, a variedades de dimensiones arbitrarias …   Wikipedia Español