Abstract
A ruled surface Φ without vanishing distribution parameter admits a non trivial geodesic mapping into a ruled surface\(\bar \Phi \), that maps the rulings of Φ into the rulings of\(\bar \Phi \), if and only if there exists a Minding-Isometry of Φ into a one-sheeted hyperboloid, which is not a hyperboloid of rotation. We also describe the geodesic mappings of a ruled surface with vanishing distribution parameter.
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