Abstract:
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.
Keywords:curvilinear three-web, regular three-web, automorphism of a three-web, infinitesimal automorphism, Chern connection of a three-web, geodesic line.
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