ar X iv : h ep - t h / 97 10 23 2 v 2 1 9 N ov 1 99 7 N = 1 Supersymmetric Quantum Mechanics on a Curved Space

The quantum mechanics of an N = 1 supersymmetric dynamical system constrained to a hypersurface embedded in the higher dimensional Euclidean space is investigated by using the projection-operator method (POM) of constrained systems. It is shown that the resulting Hamiltonian obtained by the successive operations of projection operators contains the ¯ h 2-contributing additional terms, which are completely missed when imposing constraints before the quantization. We derive the conditions the additional terms should satisfy when the N = 1 supersymmetry holds in the resulting system, and present the geometrical interpretations of these additional terms.