  It is presented a method of construction of sigma-models with target space
geometries different from conformally flat ones. The method is based on a
treating of a constancy of a coupling constant as a dynamical constraint
following as an equation of motion. In this way we build N=4 and N=8
supersymmetric four-dimensional sigma-models in d=1 with hyper-Kahler target
space possessing one isometry, which commutes with supersymmetry.
