On the harmonicity of normal almost contact metric structures

TL;DR

This paper investigates the harmonicity conditions of normal almost contact structures on Riemannian manifolds, relating their properties to curvature and structures on associated fibrations.

Contribution

It provides new formulations of harmonicity equations for almost contact structures and links their harmonicity to curvature conditions and the geometry of Morimoto fibrations.

Findings

Harmonicity equations expressed via Riemann curvature tensor

Conditions relating harmonicity of structures on total and base spaces

Insights into the geometric interplay in Morimoto fibrations

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 Riemann curvature tensor and find conditions relating the harmonicity of the almost contact and almost complex structures of the total and base spaces of the Morimoto fibration.