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Cotangent bundle - The canonical one-form

A Wisdom Archive on Cotangent bundle - The canonical one-form

Cotangent bundle - The canonical one-form

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Cotangent bundle, Cotangent bundle - Definition of the cotangent sheaf, Cotangent bundle - One-forms the cotangent sheaf, Cotangent bundle - Phase space, Cotangent bundle - Symplectic form, Cotangent bundle - The canonical one-form, Cotangent bundle - The cotangent bundle as phase space, Tangent bundle

ARTICLES RELATED TO Cotangent bundle - The canonical one-form

Cotangent bundle - The canonical one-form: Encyclopedia II - Cotangent bundle - The cotangent bundle as phase space

The cotangent bundle X=T*M, since it is a vector bundle, can be regarded as a manifold in its own right. Because of the manner in which the definition of T*M relates to the differential topology of the base space M, X possess a canonical one-form θ (also tautological one-form or symplectic potential). The exterior derivative of θ is a symplectic 2-form, out of which a non-degenerate volume form can be built for X. For example, as a result X is always an orientable manifold (mea ...

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Cotangent bundle, Cotangent bundle - One-forms the cotangent sheaf, Cotangent bundle - Definition of the cotangent sheaf, Cotangent bundle - The cotangent bundle as phase space, Cotangent bundle - The canonical one-form, Cotangent bundle - Symplectic form, Cotangent bundle - Phase space

Read more here: » Cotangent bundle: Encyclopedia II - Cotangent bundle - The cotangent bundle as phase space

Cotangent bundle - The canonical one-form: Encyclopedia II - Cotangent bundle - One-forms the cotangent sheaf

Smooth sections of the cotangent bundle are differential one-forms. Cotangent bundle - Definition of the cotangent sheaf. Let M×M be the Cartesian product of M with itself. The diagonal mapping Δ sends a point p in M to the point (p,p) of M×M. The image of Δ is called the diagonal. Let be the sheaf of germs of smooth functions on M×M which vanish on the diagonal. Then the quotient sheaf consists of equivalence classes of fu ...

See also:

Cotangent bundle, Cotangent bundle - One-forms the cotangent sheaf, Cotangent bundle - Definition of the cotangent sheaf, Cotangent bundle - The cotangent bundle as phase space, Cotangent bundle - The canonical one-form, Cotangent bundle - Symplectic form, Cotangent bundle - Phase space

Read more here: » Cotangent bundle: Encyclopedia II - Cotangent bundle - One-forms the cotangent sheaf

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