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We consider the dynamics of moving curves in three-dimensional Minkowskispace $R_1^{3}$ and deduce the evolution equations for the curvature andtorsion of the curve. Next by mapping a continuous SO(2,1) Heisenberg spinchain on the space curve in $R_1^{3}$, we show that the defocusing nonlinearSchr\"odinger equation(NLSE) can be identified with the spin chain, therebygiving a geometrical interpretation of it. The associated linear eigenvalueproblem is also obtained in a geometrical way.

Motion of Space Curves in Three-dimensional Minkowski Space $R_1^{3}$, SO(2,1) Spin Equation and Defocusing Nonlinear Schr\"odinger Equation