The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations. III

Abstract

In the canonical smooth fiber bundles $$\prod :\mathbb{R}^{n + 1} \to \mathbb{R}^n $$ endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups $$\mathbb{G}$$ (1, n) and construct $$\mathbb{G}$$ (1, n)-invariant generalized differential-geometric connections. In both regular and special cases of the representations of the considered groups $$\mathbb{G}$$ (1, n), we find all affine nonholonomic $$\Gamma _{1^ - } ,\Gamma _{2^ - } $$ , and Γ1,2-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations $$\mathbb{G}$$ (1, n) and also describe the corresponding $$\mathbb{G}$$ (1, n)invariant planar connections.