## Maps interchanging $$f$$-structures and their harmonicity.(English)Zbl 1030.53048

In this paper the authors study some remarkable classes of metric $$f$$-structures on differentiable manifolds (namely, almost Hermitian, almost contact, almost $${\mathcal{S}}$$-structures and $${\mathcal{K}}$$-structures). They state and prove the necessary condition(s) for the existence of maps commuting such structures. The paper contains several new results of geometric significance on CR-integrable manifolds and the harmonicity of such maps.

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 58E20 Harmonic maps, etc. 53C43 Differential geometric aspects of harmonic maps 53D15 Almost contact and almost symplectic manifolds

### Keywords:

$$f$$-structures; harmonic maps; CR-manifolds
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