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
Recommended Citation
Bhowmick, Aritra and Datta, Mahuya, "Existence of horizontal immersions in fat distributions" (2023). Journal Articles. 3595.
https://digitalcommons.isical.ac.in/journal-articles/3595
Comments
Open Access, Green