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Abstract
Studying of the entered earlier quasi-geodesic mappings of recurrent parabolic spaces continues. The express class of such mappings - canonical quasi-geodesic mappings is allocated. Geometrical objects, invariant under considered mappings are constructed. Metrics of the recurrent parabolic spaces admitting canonical quasi-geodesic mappings on the flat space are found. The recurrent parabolic spaces with vector fields of particular type admitting canonical quasi-geodesic mappings are indicated.
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