G-structures and material homogeneity (Q922020)

In the framework of connections on manifolds for uniform elastic bodies, the authors reformulate the mathematical theory of inhomogeneities in terms of G-structures. The material connection and material uniformity is established in order to discuss the question of homogeneity. A uniform elastic body is locally homogeneous if, and only if, the corresponding local material G-structure is flat. In this paper some cases are discussed, where the integrability problem can be solved in a rather direct manner by comparing some typical geometric characteristics of the given G-structure with the characteristics of its standard flat counterpart.