Harmonic contact metric structures, and submersions

TL;DR

This paper investigates harmonic almost contact structures within contact metric manifolds, exploring their properties when fibering over almost Hermitian manifolds and analyzing warped product structures in relation to harmonicity.

Contribution

It introduces new insights into harmonic contact metric structures and their behavior in fibrations and warped products, extending the understanding of their geometric properties.

Findings

Harmonicity conditions for contact metric structures are established.

Analysis of Boothby-Wang fibrations as examples of harmonic structures.

Relationship between harmonicity of warped products and base or fiber structures.

Abstract

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of almost contact metric warped products are also studied, relating their harmonicity to that of the almost Hermitian structure on the base or fibre.