Horizontal gradient of polynomial functions for the standard Engel structure on ${\mathbb{R}}^4$

Si Tiep Dinh, Krzysztof Kurdyka

We investigate the set $V_f$ of horizontal critical points of a polynomial function $f$ for the standard Engel structure defined by the 1-forms ${\omega }_3=d{x}_3-x_{1}d{x}_2,$ $ω_4=dx_4-x_3dx_…