| 词汇 | cotangent-bundle |
| 释义 | BETA cotangent bundlecollocation in Englishmeanings of cotangentand bundleThese words are often used together. Click on the links below to explore the meanings. cotangent noun[ C ] uk /kəʊˈtæn.dʒənt/ us /koʊˈtæn.dʒənt/ a function (= a mathematical relation) of an angle that is the reciprocal (= number) ... See more at cotangent 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 cotangent bundlecotangent bundle The cotangentbundle of a manifold is equipped with a canonical symplectic form and a canonical section (the vertical section). This transformation has an invariant form that comes from the symplectic form in the cotangentbundle of the billiard table. But why should forces take values in the cotangentbundle? Important examples of vector bundles include the tangent bundle and cotangentbundle of 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 the cotangentbundle. 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 the cotangentbundle; 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 the cotangentbundle and 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 the cotangentbundle. 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 the cotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Like the tangent bundle the cotangentbundle is 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 holomorphic cotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The cylinder is the cotangentbundle of 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 the cotangentbundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The total space of a cotangentbundle has the structure of a symplectic manifold. From Wikipedia 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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