A new optical Heisenberg ferromagnetic model for optical directional velocity magnetic flows with geometric phase

2-s2.0-85073970823 In this work, we first present the theory of Heisenberg ferromagnetic model of directional velocity magnetic flows of particles with the help of the quasi-frame in ordinary space. Afterward, we give new integrability conditions of directional velocity magnetic flows by using quasi-frame fields. Additionally, we derive the total phase for quasi-vector fields. Finally, we obtain new constructions for quasi-curvatures of directional velocity magnetic flows by Heisenberg ferromagnetic model. © 2019, Indian Association for the Cultivation of Science.