A note on N=4 supersymmetric mechanics on K\"ahler manifolds

The geometric models of N=4 supersymmetric mechanics with $(2d.2d{)}_{\text{DC}}$-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models by Alvarez-Gaum'e and Freedman. The related construction of supersymmetric mechanics whose phase space is a K"ahler supermanifold is considered. Also, its relation with antisymplectic geometry is discussed.