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词汇 frame-bundle
释义 BETA

frame bundle

collocation in English

meanings of frameand bundle


These words are often used together. Click on the links below to explore the meanings.
frame
noun[ C ]
uk /freɪm/ us /freɪm/
a border that surrounds and supports a picture, door, ...
See more at frame
bundle
noun[ C ]
uk /ˈbʌn.dəl/ us /ˈbʌn.dəl/
a number of things that have been fastened or are ...
See more at bundle


Examples of frame bundle


frame bundle
The framebundle of a smooth manifold is the one associated to its tangent bundle.
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A motivating example of a solder form is the tautological or fundamental form on the framebundle of a manifold.
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In the modern approach, this is closely related to the definition of affine connections on the framebundle.
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This gives an equivalent more geometric way of describing the connection in terms of lifting paths in the manifold to paths in the framebundle.
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Along a curve in the surface, the connection defines a first order differential equation in the framebundle.
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This enabled the curvature properties of the surface to be encoded in differential forms on the framebundle and formulas involving their exterior derivatives.
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From any vector bundle, one can construct the framebundle of bases which is a principal bundle (see below).
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It can be constructed by a method entirely analogous to that of the ordinary framebundle.
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The projection onto this subspace is defined by a differential 1-form on the orthonormal framebundle, the connection form.
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These expressions are differential 2-forms on the total space of a framebundle.
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All bundles associated with a framebundle are natural.
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At the same time, gauge gravitation theory exemplifies field theory on a principal framebundle whose gauge symmetries are general covariant transformations which are not elements of a gauge group.
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More generally still, we can consider frame bundles associated to any vector bundle, or even arbitrary principal fiber bundles.
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Tangent and frame bundles over a world manifold are natural bundles characterized by general covariant transformations.
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Wikipedia

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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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