Harmonic almost contact structures

An almost contact metric structure is parametrized by a section σ of an associated homogeneous fibre bundle, and conditions for σ to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field ξ, and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for σ reduce to those for ξ, regarded as a section of the unit tangent bundle. These include trans-Sasakian structures. On the other hand, there are examples where ξ is harmonic but σ is not a harmonic section. Many examples arise by considering hypersurfaces of almost Hermitian manifolds, with the induced almost contact structure, and comparing the harmonic section equations for both structures.