Existence and classification of maximally non-integrable distributions of derived length one

TL;DR

This paper investigates the existence and classification of maximally non-integrable tangent distributions of derived length one on manifolds, focusing on odd rank distributions and employing h-principle techniques.

Contribution

It introduces formal structures for these distributions and applies h-principles to analyze their existence and classification.

Findings

Established conditions for existence of such distributions.

Provided classification results based on formal structures.

Applied h-principles to understand non-integrability in tangent distributions.

Abstract

The h-principles for maximally non-integrable tangent distributions of derived length one on manifolds are studied in this paper. Such distributions of odd rank are dealt with. The formal structures for such distributions are introduced. From the view point of the h-principles, we discuss the existence and classification of such structures.