Screw surfaces

摘要

In this study, first of all, we express the points of a surface M in 3-dimensional Euclidean space E3 by the form of dual quaternions. Then by applying the rigid motion to all points of M, we obtain a screw surface Mψ. Here, by taking the rotation axis and translation vector in rigid motion as the same, screw motion in special case is used. Parametric expression, unit normal vector field, shape operator, Gaussian and mean curvatures of the screw surface Mψ are investigated by using differential geometric techniques. As a result, by applying rigid motion to the points of the surface M changes in differential geometric properties of M are investigated. As a special case, if the rotation angle is taken as zero then the screw surface Mψ becomes a parallel surface. In this case, all differential geometric properties obtained for screw surfaces are the same as the properties for the parallel surfaces.