2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69995A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtainedDifferential Geometry53C10; 74B20text