Cinf-structures to integrate involutive distributions
My collaborators and I have recently published two papers ( this one and this other ) in which we develop a method to obtain the integral manifolds of involutive distributions. Exploring the integral manifolds of involutive distributions contributes to a broader understanding within differential geometry, an area with ties to many other mathematical branches. Furthermore, the study of these distributions and manifolds holds relevance in physics, especially within classical mechanics and field theory. A deeper grasp of these mathematical constructs can be beneficial for ongoing research in both mathematics and physics. Given a distribution, for example \(\mathcal{Z}=\{Z_1,Z_2\}\) in \(\mathbb R^n\), the idea of our work is to complete it with a sequence of \(n-2\) vector fields \(Y_1, Y_2,Y_3,\ldots\) in such a way that - \(Y_1\) is a \(\mathcal{C}^{\infty}\)-symmetry of \(\mathcal{Z}\). - \(Y_2\) is a \(\mathcal{C}^{\infty}\)-symmetry of \(\mathcal{Z}\oplus \{X_1\}\). - \(Y_3\