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...

Descripción completa

Detalles Bibliográficos
Autores: León, Manuel de, Epstein, Marcelo, Jiménez Morales, Víctor Manuel
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
Descripción
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.