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Definition
Let "M" be a manifold and "G" a Lie group with left action "l" on "M", . Now define:which maps from the
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Conservative vector field — In vector calculus a conservative vector field is a vector field which is the gradient of a function, known in this context as a scalar potential. Conservative vector fields have the property that the line integral from one point to another is… … Wikipedia
Solenoidal vector field — In vector calculus a solenoidal vector field (also known as an incompressible vector field) is a vector field v with divergence zero at all points in the field; The fundamental theorem of vector calculus states that any vector field can be… … Wikipedia
Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… … Wikipedia
Vector calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus Derivative Change of variables Implicit differentiation Taylor s theorem Related rates … Wikipedia
Field (physics) — The magnitude of an electric field surrounding two equally charged (repelling) particles. Brighter areas have a greater magnitude. The direction of the field is not visible … Wikipedia
Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it … Wikipedia
Vector potential — In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential , which is a scalar field whose negative gradient is a given vector field.Formally, given a vector field v, a… … Wikipedia
Fundamental theorem of Riemannian geometry — In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo Riemannian manifold) there is a unique torsion free metric connection, called the Levi Civita connection of the given metric … Wikipedia
Vector boson — A vector boson is a boson with spin equal to one unit of hbar (Planck s constant divided by 2 pi). In elementary particle physics, the vector bosons currently considered to be fundamental particles are all gauge bosons. The most familiar vector… … Wikipedia
Fundamental theorem of curves — In differential geometry, the fundamental theorem of curves states that any regular curve with non zero curvature has its shape (and size) completely determined by its curvature and torsion.A curve can be described, and thereby defined, by a pair … Wikipedia
