2016/09/29 by del Pino, Alvaro, Presas, Francisco · 1 citation
#58A30 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1609.09306
In this article we study immersions of the circle that are tangent to an Engel structure D. We show that a full h-principle does exist as soon as one excludes the closed orbits of W, the kernel of D. This is sharp: we elaborate on work of Bryant and Hsu to show that curves tangent to W often conform additional isolated components that cannot be detected at a formal level. We then show that this is an exceptional phenomenon: if D is generic, curves tangent to W are not isolated anymore. We then go on to show that a full h-principle holds for immersions transverse to the Engel structure.