  The deep geometrical relationships holding among the NLS equation, the vortex
filament equation,the Heisenberg spin model, and the Schrodinger map equation
are extended to the general setting of Hermitian symmetric spaces. New results
are obtained by utilizing a generalized Hasimoto variable which arises from
applying the general theory of parallel moving frames. The example of complex
projective space CP^N= SU(N+1)/U(N) is used to illustrate the method and
results.
