Completely integrable nonlinear Schrödinger type equations on moving space curves

Using the Lamb formalism, we show that some completely integrable homogeneous and inhomogeneous nonlinear Schr\"odinger (NLS) type equations such as derivative NLS, extended NLS, higher-order NLS, inhomogeneous NLS, circularly and radially symmetric NLS, and generalized inhomogeneous radially symmetric NLS equations can be related to certain types of moving helical space curves.