Global nonautonomous Schr?dinger flows on Hermitian locally symmetric spaces

In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schr?dinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the nonautonomous (inhomogeneous) Schr?dinger flow from S¹ into a Hermitian locally symmetric space admits a unique global smooth solution, and then we address the global existence of the Cauchy problem of inhomogeneous Heisenberg spin ferromagnet system.