Abstract
On a Riemannian manifold, any parallel form is preserved by the flow of any Killing vector field with constant magnitude. As a consequence, on a 2n+1-dimensional K-contact manifold, there are no nontrivial parallel forms except of degrees 0 and 2n+1. Flat contact metrics on 3-manifolds are characterized by reducible holonomy.
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Rukimbira, P. Holonomy and contact geometry. J. Geom. 107, 125–135 (2016). https://doi.org/10.1007/s00022-015-0279-x
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DOI: https://doi.org/10.1007/s00022-015-0279-x