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Examples ofcotangent bundle

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Thecotangentbundleof a manifold is equipped with a canonical symplectic form and a canonical section (the vertical section).

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This transformation has an invariant form that comes from the symplectic form in thecotangentbundleof the billiard table.

From theCambridge English Corpus

But why should forces take values in thecotangentbundle?

From theCambridge English Corpus

Important examples of vector bundles include the tangent bundle andcotangentbundleof a smooth manifold.

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Abstractly, it is a second order operator on each exterior power of thecotangentbundle.

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A special set of coordinates can be defined on thecotangentbundle; these are called the canonical coordinates.

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If is a real differentiable function over, then is a section of thecotangentbundleand as such, we can construct a map from to.

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Likewise, the phase space can be defined more deeply using topological manifolds and thecotangentbundle.

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In symplectic geometry one is instead interested in exterior powers of thecotangentbundle.

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Like the tangent bundle thecotangentbundleis again a differentiable manifold.

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Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphiccotangentbundle.

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The cylinder is thecotangentbundleof the circle.

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Here, the canonical bundle is the same as the (holomorphic)cotangentbundle.

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In differential geometry, a one-form on a differentiable manifold is a smooth section of thecotangentbundle.

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The total space of acotangentbundlehas the structure of a symplectic manifold.

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This construction is in particular applied to thecotangentbundleof a smooth manifold.

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The metric g determines the isomorphism of the tangent and cotangent bundles.

From theCambridge English Corpus

This condition is particularly significant, being verified in all natural mechanical systems on cotangent bundles.

From theCambridge English Corpus

Vectors in the "k" th exterior power, or more precisely sections of the "k" -th exterior power of thecotangentbundle, are called differential "k" -forms.

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One of them is closely related to propagation of trajectories for symplectomorphisms of cotangent bundles.

From theCambridge English Corpus

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

单词	cotangent bundle
释义	BETA Examples ofcotangent bundle Dictionary> Examples ofcotangent bundle cotangent bundleisn’t in the Cambridge Dictionary yet. You can help! Add a definition Thecotangentbundleof a manifold is equipped with a canonical symplectic form and a canonical section (the vertical section). From theCambridge English Corpus This transformation has an invariant form that comes from the symplectic form in thecotangentbundleof the billiard table. From theCambridge English Corpus But why should forces take values in thecotangentbundle? From theCambridge English Corpus Important examples of vector bundles include the tangent bundle andcotangentbundleof a smooth manifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Abstractly, it is a second order operator on each exterior power of thecotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A special set of coordinates can be defined on thecotangentbundle; these are called the canonical coordinates. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If is a real differentiable function over, then is a section of thecotangentbundleand as such, we can construct a map from to. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Likewise, the phase space can be defined more deeply using topological manifolds and thecotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In symplectic geometry one is instead interested in exterior powers of thecotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Like the tangent bundle thecotangentbundleis again a differentiable manifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphiccotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The cylinder is thecotangentbundleof the circle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Here, the canonical bundle is the same as the (holomorphic)cotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In differential geometry, a one-form on a differentiable manifold is a smooth section of thecotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The total space of acotangentbundlehas the structure of a symplectic manifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This construction is in particular applied to thecotangentbundleof a smooth manifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The metric g determines the isomorphism of the tangent and cotangent bundles. From theCambridge English Corpus This condition is particularly significant, being verified in all natural mechanical systems on cotangent bundles. From theCambridge English Corpus Vectors in the "k" th exterior power, or more precisely sections of the "k" -th exterior power of thecotangentbundle, are called differential "k" -forms. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. One of them is closely related to propagation of trajectories for symplectomorphisms of cotangent bundles. From theCambridge English Corpus These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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