Optimal navigation strategies for microswimmers on curved manifolds

Finding the fastest path to a desired destination is vitally important task for microorganisms moving in fluid flow. We study this problem by building an analytical formalism overdamped microswimmers on curved manifolds and arbitrary flows. show that solution corresponds geodesics of Randers metric, which asymmetric Finsler metric reflects irreversible character problem. Using example spherical surface, we demonstrate swimmer performance follows "Randers policy" always beats more direct policy. A shape isochrones reveals features such as self-intersections, cusps, abrupt nonlinear effects. Our work provides link between microswimmer physics generalizations general relativity.