Abstract
In this paper, we study the evolution of the wave polarization vector in the tangent direction of the curved path. This path is assumed to be the trajectory of the propagated light beam. The polarization state of the wave is described by the unit complex transverse field component by eliminating the longitudinal field component. We obtain new relationship between the geometric phase and the parallel transportation law of the wave polarization vector of the evolving light beam in the tangent direction of the curved path. Moreover, we present a new geometric interpretation of the quasi binormal evolution of the wave polarization vector via the nonlinear Schrodinger equation of repulsive type in the tangent direction. Finally, we find a space-time nonlocal NLS reduction for equation system.