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We present simple models of N=4 supersymmetric mechanics with ordinary andmirror linear (4,4,0) multiplets that give a transparent description of HKT,CKT, and OKT geometries. These models are treated in the N=4 and N=2 superfieldapproaches, as well as in the component approach. Our study makes manifest thatthe CKT and OKT supersymmetric sigma models are distinguished from the moresimple HKT models by the presence of extra holomorphic torsions in thesupercharges.

N=4 mechanics with diverse (4,4,0) multiplets: explicit examples of HKT, CKT, and OKT geometries