Harmonic almost contact structures via the intrinsic torsion

TL;DR

This paper advances the understanding of harmonic almost contact metric structures by characterizing them through intrinsic torsion, establishing conditions for harmonicity, and providing examples of minimal energy configurations.

Contribution

It introduces new characterizations of harmonicity using intrinsic torsion and relates harmonic structures to specific classes and energy minimization.

Findings

Characterization of harmonic almost contact structures via intrinsic torsion

Conditions linking harmonicity to structure classes

Examples achieving absolute energy minimum

Abstract

We go further on the study of harmonicity for almost contact metric structures already initiated by Vergara-Diaz and Wood. By using the intrinsic torsion, we characterise harmonic almost contact metric structures in several equivalent ways and show conditions relating harmonicity and classes of almost contact metric structures. Additionally, we study the harmonicity of such structures as a map into the quotient bundle of the oriented orthonormal frames by the action of the structural group U(n)x1. Finally, by using a Bochner type formula proved by Bor and Hernandez Lamoneda, we display some examples which give the absolute minimum for the energy.