Abstract
TheClifford parallelism of the three-dimensional isotropic space J 3 (1) induces thekinematic mapping of an element of surface in J 3 (1) onto a pair of points in a fixed plane π0. By identifying a regular surface Φ with the manifold of its osculating elements of surface thekinematic image of Φ is defined and equivalent to an area preserving transformation of the plane π0. In this paper we will examine the connections between the isotropic invariants of a skew ruled surface Φ and its kinematic image. Since the striction line y of Φ exactly consists of the singular points of Φ the kinematic images of the osculating planes of y are considered in addition. In this way we obtain a correspondence between the theory of ruled surfaces and the elementary geometry of two pairs of plane curves with a common middle curve.
Published Version
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