| 词汇 | smooth-manifold |
| 释义 | BETA smooth manifoldcollocation in Englishmeanings of smoothand manifoldThese words are often used together. Click on the links below to explore the meanings. smooth adjective uk /smuːð/ us /smuːð/ having a surface or consisting of a substance that is perfectly regular and has no holes, lumps, or areas that rise or ... See more at smooth manifold noun[ C ] uk /ˈmæn.ɪ.fəʊld/ us /ˈmæn.ə.foʊld/ a pipe or closed space in a machine that has several openings, allowing liquids and gases to enter ... See more at manifold Examples of smooth manifoldsmooth manifold We call a finite-dimensional compact (respectively non-compact) smoothmanifold without boundary a closed (respectively open) manifold. Locally, a smoothmanifold can be expressed as a graph over its tangent plane. The foregoing set intersection is not a smoothmanifold of displacements as will be explained in what follows. Throughout this paper, by a manifold (map, function) we mean a smoothmanifold (map, function). This is a smoothmanifold with boundary endowed with a smooth measure. Mathematically, spacetime symmetries are usually described by smooth vector fields on a smoothmanifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The circle is characterized as a manifold by being one-dimensional, compact and connected; here the characterization, as a smoothmanifold, is up to diffeomorphism. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Every smoothmanifold can be embedded into a finite-dimensional linear space. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A smooth path in a smoothmanifold has (at every point) the tangent vector, belonging to the tangent space (attached to this point). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Important examples of vector bundles include the tangent bundle and cotangent bundle of a smoothmanifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The frame bundle of a smoothmanifold is the one associated to its tangent bundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. But if the stabilizer groups change we can not expect a smoothmanifold any longer. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A more involved example comes from differential topology, in which we have the notion of a smoothmanifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If the d-bar operator can be shown to be transverse to the zero-section, this moduli space will be a smoothmanifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Recall that a (smooth) manifold has a unique tangent bundle and a unique stable normal bundle. 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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