Mannheim Offsets of Ruled Surfaces under the 1-Parameter Motions

Abstract

In this study, the situation of Mannheim offsets of ruled surfaces under the 1-parameter motions is investigated. Firstly, relationships between geodesic Frenet trihedrons of Mannheim offsets of ruled surfaces are obtained and the relationship between the curvatures of the surface pairs is examined. Also, change of integral invariants the surface pairs under the 1-parameter motions is studied. Finally, the relevant example is given for every Mannheim offsets of ruled surfaces.