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In this paper, we define
dual curvature motion on the dual hyperbolic unit sphere H20 in the dual Lorentzian
with dual signature (+,+-) . We carry the obtained
results to the Lorentzian line space R31 by means of Study mapping.
Then we make an analysis of the orbits during the dual hyperbolic spherical
curvature motion. Finally, we find some line congruences, the family of ruled
surfaces and ruled surfaces in R31.