Linear non-holonomic manifolds of constant defect in \(E^ n\) (Q1896720)

Given a linear nonholonomic \(\ell\)-dimensional manifold \(V^\ell\) (in \(n\)-dimensional Euclidean space \(E^n)\), let \(T_{0,L}^{\text{ext}} (x_0)\), \(T_{0,R}^{\text{ext}} (x_0)\) denote the left space of nullity and right space of nullity of \(V^\ell\), respectively, at a point \(x_0 \in E^n\). The authors study the integrability and the leaves of the \(k\)-dimensional distribution \(T_0^{\text{ext}}\) in the special setting where \(T_{0,L}^{\text{ext}} = T_{0,R}^{\text{ext}} = T_0^{\text{ext}}\), \(\dim T_0^{\text{ext}} = k\). The method consists of using the Christoffel symbols and the spaces of nullity.