Although acoustics is one of the disciplines of mechanics, its a�?geometrizationa�? is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the a�?covarianta�? approach. The contribution of this article is to relate this approach to the extension of geodesic curves (1-dimensional submanifold) to auto-parallel submanifolds (n-dimensional submanifold).
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