Publication: Characteristic distribution: An application to material bodies
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Date
2018
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info:eu-repo/semantics/openAccess
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Publisher
Elsevier
Abstract
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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Keywords
Smooth distribution, Singular foliation, Groupoid, Uniformity, Material groupoid
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Center
Facultad de Ciencias
Department
Matemáticas Fundamentales