covariantly
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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
Pp-wave spacetime — In general relativity, the pp wave spacetimes, or pp waves for short, are an important family of exact solutions of Einstein s field equation. These solutions model radiation moving at the speed of light. This radiation may consist of:*… … Wikipedia
Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … 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
Gauge theory — For a generally accessible and less technical introduction to the topic, see Introduction to gauge theory. In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations … Wikipedia
Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… … Wikipedia
Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… … Wikipedia
Stress-energy tensor — The stress energy tensor (sometimes stress energy momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of … Wikipedia
Einstein notation — In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention useful when dealing with coordinate formulas. It was introduced by Albert Einstein in 1916 … 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
