Сurvilinear Three-Webs with Automorphisms

A general form of the equation of a curvilinear three-web admitting a one-parameter family of automorphisms ( \(AW\) -webs) is found. It is proved that the trajectories of automorphisms of an \(AW\) -web are geodesics of its Chern connection. All \(AW\) -webs are found for which one of the covariant derivatives of curvature is zero.