Generalized Zermelo Navigation on Hermitian Manifolds with a Critical Wind

We study the Zermelo navigation problem on Hermitian manifolds (M, h) in the presence of a critical perturbation W determined by a complex velocity vector field such that $0<||W\left(z\right)|{|}_h=||u\left(z\right)|{|}_h\le 1$, admitting space dependence of a ship's relative speed $||u\left(z\right)|{|}_h$, with application of complex Finsler metric of complex Kropina type. We discuss the geodesics corresponding to the critical solutions to Zermelo's problem and we find the necessary and sufficient conditions for the obtained locally projectively flat solutions.