Existence of Horizontal Immersions in Fat Distributions

Abstract

Contact structures, as well as their holomorphic and quaternionic counterparts are the primary examples of strongly bracket generating (or fat) distributions. In this article we associate a numerical invariant to corank $2$ fat distribution on manifolds, referred to as \emph{degree} of the distribution. The real distribution underlying a holomorphic contact structure is of degree $2$. Using Gromov's sheaf theoretic and analytic techniques of $h$-principle, we prove the existence of horizontal immersions of an arbitrary manifold into degree $2$ fat distributions and the quaternionic contact structures. We also study immersions of a contact manifold inducing the given contact structure.

Minor changes according to referee report. Final version. To appear in Int. J. Math

References in corpus (2)

• Holomorphic Legendrian curves
• The Oka principle for holomorphic Legendrian curves in ${\mathbb{C}}^{2n+1}$

Cited by in corpus (1)

• The $h$-Principle for Maps Transverse to Bracket-Generating Distributions