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We derive and discuss a new type of N=2 supersymmetric quantum mechanicalsigma models which appear when the superfield action of the (1,2,1) multipletsis modified by adding an imaginary antisymmetric tensor to the target spacemetric, thus completing the latter to a non-symmetric Hermitian metric. Thesemodels are not equivalent to the standard de Rham sigma models, but are relatedto them through a certain special similarity transformation of thesupercharges. On the other hand, they can be obtained by a Hamiltonianreduction from the complex supersymmetric N=2 sigma models built on themultiplets (2,2,0) and describing the Dolbeault complex on the manifolds withproper isometries. We study in detail the extremal two-dimensional case, whenthe target space metric is defined solely by the antisymmetric tensor, and showthat the corresponding quantum systems reveal a hidden N=4 supersymmetry.

Quasicomplex N=2, d=1 Supersymmetric Sigma Models