The harmonicity of nearly cosymplectic structures

TL;DR

This paper investigates the harmonicity of nearly cosymplectic almost contact structures on Riemannian manifolds, establishing curvature identities that prove their harmonicity and extending previous work on nearly-Kähler structures.

Contribution

It introduces curvature identities that demonstrate the harmonicity of nearly cosymplectic structures, expanding the understanding of harmonic sections in almost contact geometry.

Findings

Curvature identities imply harmonicity of nearly cosymplectic structures

Extension of harmonicity results from nearly-Kähler to nearly cosymplectic structures

Provides a framework for analyzing harmonic sections in almost contact geometry

Abstract

Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold and prove curvature identities which imply the harmonicity of their parametrizing section, thus complementing earlier results on nearly-K{\"a}hler almost complex structures.