Harmonic almost contact structures via the intrinsic torsion. (English) Zbl 1219.53075
The paper continues the study of harmonicity for almost contact metric structures, initiated by E. Vergara-Diaz and C. M. Wood. By using the intrinsic torsion, harmonic almost contact metric structures are characterized in several equivalent ways, and conditions are shown relating harmonicity and classes of almost contact metric structures. Harmonicity of such structures, considered as a map into the quotient bundle of the oriented orthonormal frames by the action of the structural group \(U(n)\times1\), is investigated. Finally, by using a Bochner type formula proved in [G. Bor and L. Hernández Lamoneda, Differ. Geom. Appl. 15, No. 3, 265–286 (2001; Zbl 1036.53015)], several examples are derived which give the absolute minimum for the energy.
Reviewer: Vladimir Balan (Bucureşti)
MSC:
| 53D15 | Almost contact and almost symplectic manifolds |
| 53C43 | Differential geometric aspects of harmonic maps |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
Citations:
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