Higher order flatness of immersed manifolds (Q1293410)

The Andreotti number \({\mathcal A}(M)\) of a \(C^\infty\)-manifold \(M\) is defined as the smallest nonnegative number \(r\) such that the \(r\)-th order jet bundle of \(M\) admits a flat structure. If no such \(r\) exists, \({\mathcal A}(M)\) is defined to be \(\infty\). The author proves that a \(C^\infty\)-manifold \(M\) which can be immersed into the Euclidean space with codimension one has finite Andreotti number \({\mathcal A}(M)\). He gives an example of a 4-dimensional manifold \(M\) which can be immersed in \(\mathbb{R}^6\) and for which \({\mathcal A}(M)=\infty\).