Harmonicity of normal almost contact metric structures
Abstract
We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of the curvature tensor and find conditions relating the harmonicity of the almost contact metric and almost complex structures of the total and base spaces of the Morimoto fibration. We apply these results to homogeneous principal circle bundles over generalised flag manifolds, in particular Aloff-Wallach spaces, to mass-produce harmonic almost contact metric structures.
Cite
@article{arxiv.2310.11089,
title = {Harmonicity of normal almost contact metric structures},
author = {M. Benyounes and T. Levasseur and E. Loubeau and E. Vergara-Diaz},
journal= {arXiv preprint arXiv:2310.11089},
year = {2026}
}
Comments
26 pages, this supersedes arXiv:1109.1964 [math.DG], with four authors and a slightly different title. It non only corrects arXiv:1109.1964 [math.DG] but also vastly improves it with a systematic approach to homogeneous principal circle bundles over generalised flag manifolds