Characteristic distribution: An application to material bodies
Associated to each material body B there exists a groupoid (B) consisting of all the material isomorphisms connecting the points of B. The uniformity character of B is reflected in the properties of (B): B is uniform if, and only if, (B) is transitive. Smooth uniformity corresponds to a Lie groupoid...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/12557 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/12557 |
| Access Level: | acceso abierto |
| Palabra clave: | Smooth distribution Singular foliation Groupoid Uniformity Material groupoid |
| Sumario: | Associated to each material body B there exists a groupoid (B) consisting of all the material isomorphisms connecting the points of B. The uniformity character of B is reflected in the properties of (B): B is uniform if, and only if, (B) is transitive. Smooth uniformity corresponds to a Lie groupoid and, specifically, to a Lie subgroupoid of the groupoid 1 (B,B) of 1- jets of B. We consider a general situation when (B) is only an algebraic subgroupoid. Even in this case, we can cover B by a material foliation whose leaves are transitive. The same happens with (B) and the corresponding leaves generate transitive Lie groupoids (roughly speaking, the leaves covering B). This result opens the possibility to study the homogeneity of general material bodies using geometric instruments. |
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