Existence of horizontal immersions in fat distributions

Article Type

Research Article

Publication Title

International Journal of Mathematics

Abstract

Contact structures, as well as their holomorphic and quaternionic counterparts, are the primary examples of strongly bracket generating (or fat) distributions. In this paper, we associate a numerical invariant to corank-2 fat distribution on manifolds, referred to as the 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 isocontact immersions, i.e. immersions that pull back a fat distribution to a given contact structure.

DOI

https://10.1142/S0129167X23500568

Publication Date

9-1-2023

Comments

Open Access, Green

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