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Examples ofvector bundle
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In fact, for the following application, we will immediately come back to avectorbundlesituation.
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Now choose a partition of unity subordinate to a cover of byvectorbundlecharts.
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However, is covered byvectorbundlecharts of this type.
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The control theorem holds for the weightvectorbundle.
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First of all we discuss some questions of smoothing the sections of avectorbundle.
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Together, these two ingredients show that a proper group action is equivalent in a neighbourhood of each orbit to a linear action on avectorbundle.
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A realvectorbundleadmits an almost complex structure if and only if it is the underlying real bundle of a complexvectorbundle.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These are called the transition functions (or the coordinate transformations) of thevectorbundle.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is similar to the cobordism ring of oriented manifolds, except that the manifolds also have avectorbundle.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In topology, differential geometry, and algebraic geometry, it is often important to count how many linearly independent sections avectorbundlehas.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Connections (gauge connection) define this principal bundle, yielding a covariant derivative in each associatedvectorbundle.
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This example is from Wikipedia and may be reused under a CC BY-SA license.If the fiber bundle is avectorbundle, then the notion of parallel transport must be linear.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The fiber of the correspondingvectorbundleover "x" is then the range of "f" ("x").
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This example is from Wikipedia and may be reused under a CC BY-SA license.More generally, differential geometers consider spaces with avectorbundleand an arbitrary affine connection which is not defined in terms of a metric.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Vectorbundlemorphisms are a special case of the notion of a bundle map between fiber bundles, and are also often called (vector)bundlehomomorphisms.
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This example is from Wikipedia and may be reused under a CC BY-SA license.More generally still, we can consider frame bundles associated to anyvectorbundle, or even arbitrary principal fiber bundles.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The tangent bundle to a manifold is the prototypical example of avectorbundle(a fiber bundle whose fibers are vector spaces).
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This example is from Wikipedia and may be reused under a CC BY-SA license.The tangent bundle is an example of a more general construction called avectorbundle(which is itself a specific kind of fiber bundle).
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This example is from Wikipedia and may be reused under a CC BY-SA license.The former is and the latter is a -dimensionalvectorbundleover.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Such a sheaf is always locally free of the same rank as the rank of thevectorbundle.
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This example is from Wikipedia and may be reused under a CC BY-SA license.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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