Holonomy of K-contact sub-Riemannian manifolds

TL;DR

This paper investigates the horizontal holonomy group of K-contact sub-Riemannian manifolds, revealing it either matches the Riemannian holonomy or is a specific subgroup, with discussions on parallel horizontal spinors and examples.

Contribution

It characterizes the structure of the horizontal holonomy group in K-contact sub-Riemannian manifolds and explores implications for parallel horizontal spinors.

Findings

Horizontal holonomy group equals Riemannian holonomy or a codimension-one subgroup.

Discussion on existence of parallel horizontal spinors.

Provides examples and explores consequences of the holonomy structure.

Abstract

It is shown that the horizontal holonomy group of a K-contact sub-Riemannian manifold either coincides with the holonomy group of a Riemannian manifold, or it is a codimension-one normal subgroup of the later group. The question of existence of parallel horizontal spinors, examples, and consequences are discussed.