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contravariant derivative

См. также в других словарях:

  • Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …   Wikipedia

  • Exterior derivative — In differential geometry, the exterior derivative extends the concept of the differential of a function, which is a form of degree zero, to differential forms of higher degree. Its current form was invented by Élie Cartan.The exterior derivative… …   Wikipedia

  • Covariant transformation — See also Covariance and contravariance of vectors In physics, a covariant transformation is a rule (specified below), that describes how certain physical entities change under a change of coordinate system. In particular the term is used for… …   Wikipedia

  • Euclidean vector — This article is about the vectors mainly used in physics and engineering to represent directed quantities. For mathematical vectors in general, see Vector (mathematics and physics). For other uses, see vector. Illustration of a vector …   Wikipedia

  • Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …   Wikipedia

  • Introduction to mathematics of general relativity — An understanding of calculus and differential equations is necessary for the understanding of nonrelativistic physics. In order to understand special relativity one also needs an understanding of tensor calculus. To understand the general theory… …   Wikipedia

  • Gradient — In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.A generalization of the gradient for… …   Wikipedia

  • Mathematics of general relativity — For a generally accessible and less technical introduction to the topic, see Introduction to mathematics of general relativity. General relativity Introduction Mathematical formulation Resources …   Wikipedia

  • Covariance and contravariance of vectors — For other uses of covariant or contravariant , see covariance and contravariance. In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities… …   Wikipedia

  • Pullback (differential geometry) — Suppose that φ : M → N is a smooth map between smooth manifolds M and N ; then there is an associated linear map from the space of 1 forms on N (the linear space of sections of the cotangent bundle) to the space of 1 forms on M . This linear map… …   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

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