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Characteristic distribution: An application to material bodies.
- Source :
-
Journal of Geometry & Physics . Apr2018, Vol. 127, p19-31. 13p. - Publication Year :
- 2018
-
Abstract
- Associated to each material body B there exists a groupoid Ω B consisting of all the material isomorphisms connecting the points of B . The uniformity character of B is reflected in the properties of Ω B : B is uniform if, and only if, Ω B is transitive. Smooth uniformity corresponds to a Lie groupoid and, specifically, to a Lie subgroupoid of the groupoid Π 1 B , B of 1-jets of B . We consider a general situation when Ω 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 Ω 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 127
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 128452270
- Full Text :
- https://doi.org/10.1016/j.geomphys.2018.01.021