Holonomy of K-contact sub-Riemannian manifolds

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.

15 pages; the final version accepted for publication in Annali di Matematica Pura ed Applicata (1923 -)