Abstract:
In this thesis we study Gromov's h-Principle in the context of immersions horizontal to a given distribution. We prove Gromov's overregularity theorem in full generality and extend it to other classes of maps, e.g, isocontact and partially horizontal immersions. Using this, we prove the h-principle for horizontal and isocontact immersions into certain fat distributions. We also obtain the existence of such maps by resolving the obstruction theoretic problem. We have proved some new h-principles for partially horizontal immersions as well.
