Lines on holomorphic contact manifolds and a generalization of $(2,3,5)$-distributions to higher dimensions

TL;DR

This paper extends the classical correspondence between holomorphic (2,3,5)-distributions and lines on contact manifolds to higher dimensions, introducing a new class of distributions with growth vector (2m, 3m, 3m+2).

Contribution

It generalizes the known (2,3,5) distribution correspondence to higher dimensions by studying nondegenerate lines on holomorphic contact manifolds and defining new distributions with specific growth vectors.

Findings

Established a higher-dimensional correspondence between lines on contact manifolds and distributions.

Defined and characterized distributions with growth vector (2m, 3m, 3m+2).

Extended classical geometric structures to a broader, higher-dimensional setting.

Abstract

Since the celebrated work by Cartan, distributions with \nobreak{small} growth vector $(2,3,5)$ have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic $(2,3,5)$-distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5. We generalize this correspondence to higher dimensions by studying nondegenerate lines on holomorphic contact manifolds and the corresponding class of distributions of small growth vector $(2m, 3m, 3m+2)$ for any positive integer $m$.