Generalized Zermelo navigation on Hermitian manifolds with a critical wind (Q681271)

The aim of the paper is to develop a geometric description of the Zermelo problem in a complex setting. Considering a nonzero speed \({\| u(z)\|}_h \), varying in magnitude, on a Hermitian manifold \((M,h)\) for a complex perturbation \(W\), with \(0 < \| W(z)\|_h = \| u(z)\|_h\leq 1\) everywhere on \(M\), the authors obtain that the solutions of such a generalized Zermelo navigation problem can be complex Finsler metrics of Kropina type, under some restrictions. They investigate the projectively related complex Kropina metrics, the geodesics corresponding to the critical solutions to the Zermelo navigation problem, in particular the Berwald-Kropina case. Some necessary and sufficient conditions for the locally projectively flat solutions obtained are given.